A 6-tuple ( \mathbf{C}, \sqcup, 1, \alpha, \lambda, \rho ) consisting of
a category \mathbf{C},
a functor \sqcup: \mathbf{C} \times \mathbf{C} \rightarrow \mathbf{C},
an object 1 \in \mathbf{C},
a natural isomorphism \alpha_{a,b,c}: a \sqcup (b \sqcup c) \cong (a \sqcup b) \sqcup c,
a natural isomorphism \lambda_{a}: 1 \sqcup a \cong a,
a natural isomorphism \rho_{a}: a \sqcup 1 \cong a,
is called a cocartesian category, if
for all objects a,b,c,d, the pentagon identity holds:
(\alpha_{a,b,c} \sqcup \mathrm{id}_d) \circ \alpha_{a,b \sqcup c, d} \circ ( \mathrm{id}_a \sqcup \alpha_{b,c,d} ) = \alpha_{a \sqcup b, c, d} \circ \alpha_{a,b,c \sqcup d},
for all objects a,c, the triangle identity holds:
( \rho_a \sqcup \mathrm{id}_c ) \circ \alpha_{a,1,c} = \mathrm{id}_a \sqcup \lambda_c.
The corresponding GAP property is given by IsCocartesianCategory
.
‣ CocartesianBraiding ( a, b ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( a \sqcup b, b \sqcup a ).
The arguments are two objects a,b. The output is the braiding B_{a,b}: a \sqcup b \rightarrow b \sqcup a.
‣ CocartesianBraidingWithGivenCoproducts ( s, a, b, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( a \sqcup b, b \sqcup a ).
The arguments are an object s = a \sqcup b, two objects a,b, and an object r = b \sqcup a. The output is the braiding B_{a,b}: a \sqcup b \rightarrow b \sqcup a.
‣ CocartesianBraidingInverse ( a, b ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( b \sqcup a, a \sqcup b ).
The arguments are two objects a,b. The output is the inverse braiding B_{a,b}^{-1}: b \sqcup a \rightarrow a \sqcup b.
‣ CocartesianBraidingInverseWithGivenCoproducts ( s, a, b, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( b \sqcup a, a \sqcup b ).
The arguments are an object s = b \sqcup a, two objects a,b, and an object r = a \sqcup b. The output is the inverse braiding B_{a,b}^{-1}: b \sqcup a \rightarrow a \sqcup b.
‣ CoproductOnMorphisms ( alpha, beta ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(a \sqcup b, a' \sqcup b')
The arguments are two morphisms \alpha: a \rightarrow a', \beta: b \rightarrow b'. The output is the coproduct \alpha \sqcup \beta.
‣ CoproductOnMorphismsWithGivenCoproducts ( s, alpha, beta, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(a \sqcup b, a' \sqcup b')
The arguments are an object s = a \sqcup b, two morphisms \alpha: a \rightarrow a', \beta: b \rightarrow b', and an object r = a' \sqcup b'. The output is the coproduct \alpha \sqcup \beta.
‣ CocartesianAssociatorRightToLeft ( a, b, c ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( a \sqcup (b \sqcup c), (a \sqcup b) \sqcup c ).
The arguments are three objects a,b,c. The output is the associator \alpha_{a,(b,c)}: a \sqcup (b \sqcup c) \rightarrow (a \sqcup b) \sqcup c.
‣ CocartesianAssociatorRightToLeftWithGivenCoproducts ( s, a, b, c, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( a \sqcup (b \sqcup c), (a \sqcup b) \sqcup c ).
The arguments are an object s = a \sqcup (b \sqcup c), three objects a,b,c, and an object r = (a \sqcup b) \sqcup c. The output is the associator \alpha_{a,(b,c)}: a \sqcup (b \sqcup c) \rightarrow (a \sqcup b) \sqcup c.
‣ CocartesianAssociatorLeftToRight ( a, b, c ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( (a \sqcup b) \sqcup c \rightarrow a \sqcup (b \sqcup c) ).
The arguments are three objects a,b,c. The output is the associator \alpha_{(a,b),c}: (a \sqcup b) \sqcup c \rightarrow a \sqcup (b \sqcup c).
‣ CocartesianAssociatorLeftToRightWithGivenCoproducts ( s, a, b, c, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( (a \sqcup b) \sqcup c \rightarrow a \sqcup (b \sqcup c) ).
The arguments are an object s = (a \sqcup b) \sqcup c, three objects a,b,c, and an object r = a \sqcup (b \sqcup c). The output is the associator \alpha_{(a,b),c}: (a \sqcup b) \sqcup c \rightarrow a \sqcup (b \sqcup c).
‣ CocartesianLeftUnitor ( a ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}(1 \sqcup a, a)
The argument is an object a. The output is the left unitor \lambda_a: 1 \sqcup a \rightarrow a.
‣ CocartesianLeftUnitorWithGivenCoproduct ( a, s ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(1 \sqcup a, a)
The arguments are an object a and an object s = 1 \sqcup a. The output is the left unitor \lambda_a: 1 \sqcup a \rightarrow a.
‣ CocartesianLeftUnitorInverse ( a ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}(a, 1 \sqcup a)
The argument is an object a. The output is the inverse of the left unitor \lambda_a^{-1}: a \rightarrow 1 \sqcup a.
‣ CocartesianLeftUnitorInverseWithGivenCoproduct ( a, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(a, 1 \sqcup a)
The argument is an object a and an object r = 1 \sqcup a. The output is the inverse of the left unitor \lambda_a^{-1}: a \rightarrow 1 \sqcup a.
‣ CocartesianRightUnitor ( a ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}(a \sqcup 1, a)
The argument is an object a. The output is the right unitor \rho_a: a \sqcup 1 \rightarrow a.
‣ CocartesianRightUnitorWithGivenCoproduct ( a, s ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(a \sqcup 1, a)
The arguments are an object a and an object s = a \sqcup 1. The output is the right unitor \rho_a: a \sqcup 1 \rightarrow a.
‣ CocartesianRightUnitorInverse ( a ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}(a, a \sqcup 1)
The argument is an object a. The output is the inverse of the right unitor \rho_a^{-1}: a \rightarrow a \sqcup 1.
‣ CocartesianRightUnitorInverseWithGivenCoproduct ( a, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(a, a \sqcup 1)
The arguments are an object a and an object r = a \sqcup 1. The output is the inverse of the right unitor \rho_a^{-1}: a \rightarrow a \sqcup 1.
‣ CocartesianCodiagonal ( a, n ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(\sqcup_{i=1}^n a, a).
The arguments are an object a and an integer n \geq 0. The output is the codiagonal morphism from the n-fold cocartesian multiple \sqcup_{i=1}^n a to a. If the category does not support empty limits, n must be not be 0.
‣ CocartesianCodiagonalWithGivenCocartesianMultiple ( a, n, b ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(b, a)
The arguments are an object a, an integer n, and an object b equal to the n-fold cocartesian multiple \sqcup_{i=1}^n a of a. The output is the codiagonal morphism from b to a.
‣ LeftCocartesianCodistributivityExpanding ( a, L ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( a \sqcup (b_1 \times \dots \times b_n), (a \sqcup b_1) \times \dots \times (a \sqcup b_n) )
The arguments are an object a and a list of objects L = (b_1, \dots, b_n). The output is the left distributivity morphism a \sqcup (b_1 \times \dots \times b_n) \rightarrow (a \sqcup b_1) \times \dots \times (a \sqcup b_n).
‣ LeftCocartesianCodistributivityExpandingWithGivenObjects ( s, a, L, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( s, r )
The arguments are an object s = a \sqcup (b_1 \times \dots \times b_n), an object a, a list of objects L = (b_1, \dots, b_n), and an object r = (a \sqcup b_1) \times \dots \times (a \sqcup b_n). The output is the left distributivity morphism s \rightarrow r.
‣ LeftCocartesianCodistributivityFactoring ( a, L ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( (a \sqcup b_1) \times \dots \times (a \sqcup b_n), a \sqcup (b_1 \times \dots \times b_n) )
The arguments are an object a and a list of objects L = (b_1, \dots, b_n). The output is the left distributivity morphism (a \sqcup b_1) \times \dots \times (a \sqcup b_n) \rightarrow a \sqcup (b_1 \times \dots \times b_n).
‣ LeftCocartesianCodistributivityFactoringWithGivenObjects ( s, a, L, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( s, r )
The arguments are an object s = (a \sqcup b_1) \times \dots \times (a \sqcup b_n), an object a, a list of objects L = (b_1, \dots, b_n), and an object r = a \sqcup (b_1 \times \dots \times b_n). The output is the left distributivity morphism s \rightarrow r.
‣ RightCocartesianCodistributivityExpanding ( L, a ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( (b_1 \times \dots \times b_n) \sqcup a, (b_1 \sqcup a) \times \dots \times (b_n \sqcup a) )
The arguments are a list of objects L = (b_1, \dots, b_n) and an object a. The output is the right distributivity morphism (b_1 \times \dots \times b_n) \sqcup a \rightarrow (b_1 \sqcup a) \times \dots \times (b_n \sqcup a).
‣ RightCocartesianCodistributivityExpandingWithGivenObjects ( s, L, a, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( s, r )
The arguments are an object s = (b_1 \times \dots \times b_n) \sqcup a, a list of objects L = (b_1, \dots, b_n), an object a, and an object r = (b_1 \sqcup a) \times \dots \times (b_n \sqcup a). The output is the right distributivity morphism s \rightarrow r.
‣ RightCocartesianCodistributivityFactoring ( L, a ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( (b_1 \sqcup a) \times \dots \times (b_n \sqcup a), (b_1 \times \dots \times b_n) \sqcup a)
The arguments are a list of objects L = (b_1, \dots, b_n) and an object a. The output is the right distributivity morphism (b_1 \sqcup a) \times \dots \times (b_n \sqcup a) \rightarrow (b_1 \times \dots \times b_n) \sqcup a .
‣ RightCocartesianCodistributivityFactoringWithGivenObjects ( s, L, a, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( s, r )
The arguments are an object s = (b_1 \sqcup a) \times \dots \times (b_n \sqcup a), a list of objects L = (b_1, \dots, b_n), an object a, and an object r = (b_1 \times \dots \times b_n) \sqcup a. The output is the right distributivity morphism s \rightarrow r.
A cocartesian category \mathbf{C} which has for each functor - \sqcup b: \mathbf{C} \rightarrow \mathbf{C} a left adjoint (denoted by \mathrm{Coexponential}(-,b)) is called a coclosed cocartesian category.
The corresponding GAP property is called IsCocartesianCoclosedCategory
.
‣ CoexponentialOnObjects ( a, b ) | ( operation ) |
Returns: an object
The arguments are two objects a,b. The output is the coexponential object \mathrm{Coexponential}(a,b).
‣ CoexponentialOnMorphisms ( alpha, beta ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( \mathrm{Coexponential}(a,b'), \mathrm{Coexponential}(a',b) )
The arguments are two morphisms \alpha: a \rightarrow a', \beta: b \rightarrow b'. The output is the coexponential morphism \mathrm{Coexponential}(\alpha,\beta): \mathrm{Coexponential}(a,b') \rightarrow \mathrm{Coexponential}(a',b).
‣ CoexponentialOnMorphismsWithGivenCoexponentials ( s, alpha, beta, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( s, r )
The arguments are an object s = \mathrm{Coexponential}(a,b'), two morphisms \alpha: a \rightarrow a', \beta: b \rightarrow b', and an object r = \mathrm{Coexponential}(a',b). The output is the coexponential morphism \mathrm{Coexponential}(\alpha,\beta): \mathrm{Coexponential}(a,b') \rightarrow \mathrm{Coexponential}(a',b).
‣ CocartesianRightEvaluationMorphism ( a, b ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( b, a \sqcup \mathrm{Coexponential}(b,a) ).
The arguments are two objects a, b. The output is the coclosed right evaluation morphism \mathrm{cocaev}_{a,b}: b \rightarrow a \sqcup \mathrm{Coexponential}(b,a), i.e., the unit of the coexponential-coproduct adjunction.
‣ CocartesianRightEvaluationMorphismWithGivenRange ( a, b, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( b, r ).
The arguments are two objects a,b and an object r = a \sqcup \mathrm{Coexponential}(b,a). The output is the coclosed right evaluation morphism \mathrm{cocaev}_{a,b}: b \rightarrow a \sqcup \mathrm{Coexponential}(b,a), i.e., the unit of the coexponential-coproduct adjunction.
‣ CocartesianRightCoevaluationMorphism ( a, b ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( \mathrm{Coexponential}(a \sqcup b, a), b ).
The arguments are two objects a,b. The output is the coclosed right coevaluation morphism \mathrm{cocacoev}_{a,b}: \mathrm{Coexponential}(a \sqcup b, a) \rightarrow b, i.e., the counit of the coexponential-coproduct adjunction.
‣ CocartesianRightCoevaluationMorphismWithGivenSource ( a, b, s ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( s, b ).
The arguments are two objects a,b and an object s = \mathrm{Coexponential}(a \sqcup b, a). The output is the coclosed right coevaluation morphism \mathrm{cocacoev}_{a,b}: \mathrm{Coexponential}(a \sqcup b, a) \rightarrow b, i.e., the unit of the coexponential-coproduct adjunction.
‣ CoproductToCoexponentialRightAdjunctMorphism ( b, c, g ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( \mathrm{Coexponential}(a,b), c ).
The arguments are two objects b,c and a morphism g: a \rightarrow b \sqcup c. The output is a morphism f: \mathrm{Coexponential}(a,b) \rightarrow c corresponding to g under the coexponential-coproduct adjunction.
‣ CoproductToCoexponentialRightAdjunctMorphismWithGivenCoexponential ( b, c, g, i ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( i, c ).
The arguments are two objects b,c, a morphism g: a \rightarrow b \sqcup c and an object i = \mathrm{Coexponential}(a,b). The output is a morphism f: \mathrm{Coexponential}(a,b) \rightarrow c corresponding to g under the coexponential-coproduct adjunction.
‣ CoexponentialToCoproductRightAdjunctMorphism ( a, b, f ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(a, b \sqcup c).
The arguments are two objects a,b and a morphism f: \mathrm{Coexponential}(a,b) \rightarrow c. The output is a morphism g: a \rightarrow b \sqcup c corresponding to f under the coexponential-coproduct adjunction.
‣ CoexponentialToCoproductRightAdjunctMorphismWithGivenCoproduct ( a, b, f, t ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( a, t ).
The arguments are two objects a,b, a morphism f: \mathrm{Coexponential}(a,b) \rightarrow c and an object t = b \sqcup c. The output is a morphism g: a \rightarrow t corresponding to f under the coexponential-coproduct adjunction.
‣ CocartesianLeftEvaluationMorphism ( a, b ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( b, \mathrm{Coexponential}(b,a) \sqcup a ).
The arguments are two objects a, b. The output is the coclosed left evaluation morphism \mathrm{cocaev}_{a,b}: b \rightarrow \mathrm{Coexponential}(b,a) \sqcup a, i.e., the unit of the coexponential-coproduct adjunction.
‣ CocartesianLeftEvaluationMorphismWithGivenRange ( a, b, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( b, r ).
The arguments are two objects a,b and an object r = \mathrm{Coexponential}(b,a) \sqcup a. The output is the coclosed left evaluation morphism \mathrm{cocaev}_{a,b}: b \rightarrow \mathrm{Coexponential}(b,a) \sqcup a, i.e., the unit of the coexponential-coproduct adjunction.
‣ CocartesianLeftCoevaluationMorphism ( a, b ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( \mathrm{Coexponential}(b \sqcup a, a), b ).
The arguments are two objects a,b. The output is the coclosed left coevaluation morphism \mathrm{cocacoev}_{a,b}: \mathrm{Coexponential}(b \sqcup a, a) \rightarrow b, i.e., the counit of the coexponential-coproduct adjunction.
‣ CocartesianLeftCoevaluationMorphismWithGivenSource ( a, b, s ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( s, b ).
The arguments are two objects a,b and an object s = \mathrm{Coexponential}(b \sqcup a, a). The output is the coclosed left coevaluation morphism \mathrm{cocacoev}_{a,b}: \mathrm{Coexponential}(b \sqcup a, a) \rightarrow b, i.e., the unit of the coexponential-coproduct adjunction.
‣ CoproductToCoexponentialLeftAdjunctMorphism ( b, c, g ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( \mathrm{Coexponential}(a,c), b ).
The arguments are two objects b,c and a morphism g: a \rightarrow b \sqcup c. The output is a morphism f: \mathrm{Coexponential}(a,c) \rightarrow b corresponding to g under the coexponential-coproduct adjunction.
‣ CoproductToCoexponentialLeftAdjunctMorphismWithGivenCoexponential ( b, c, g, i ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( i, b ).
The arguments are two objects b,c, a morphism g: a \rightarrow b \sqcup c and an object i = \mathrm{Coexponential}(a,c). The output is a morphism f: \mathrm{Coexponential}(a,c) \rightarrow b corresponding to g under the coexponential-coproduct adjunction.
‣ CoexponentialToCoproductLeftAdjunctMorphism ( a, c, f ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(a, b \sqcup c).
The arguments are two objects a,c and a morphism f: \mathrm{Coexponential}(a,c) \rightarrow b. The output is a morphism g: a \rightarrow b \sqcup c corresponding to f under the coexponential-coproduct adjunction.
‣ CoexponentialToCoproductLeftAdjunctMorphismWithGivenCoproduct ( a, c, f, t ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( a, t ).
The arguments are two objects a,c, a morphism f: \mathrm{Coexponential}(a,c) \rightarrow b and an object t = b \sqcup c. The output is a morphism g: a \rightarrow t corresponding to f under the coexponential-coproduct adjunction.
‣ CocartesianPreCoComposeMorphism ( a, b, c ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( \mathrm{Coexponential}(a,c), \mathrm{Coexponential}(b,c) \sqcup \mathrm{Coexponential}(a,b) ).
The arguments are three objects a,b,c. The output is the precocomposition morphism \mathrm{CocartesianPreCoComposeMorphism}_{a,b,c}: \mathrm{Coexponential}(a,c) \rightarrow \mathrm{Coexponential}(b,c) \sqcup \mathrm{Coexponential}(a,b).
‣ CocartesianPreCoComposeMorphismWithGivenObjects ( s, a, b, c, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( s, r ).
The arguments are an object s = \mathrm{Coexponential}(a,c), three objects a,b,c, and an object r = \mathrm{Coexponential}(a,b) \sqcup \mathrm{Coexponential}(b,c). The output is the precocomposition morphism \mathrm{CocartesianPreCoComposeMorphismWithGivenObjects}_{a,b,c}: \mathrm{Coexponential}(a,c) \rightarrow \mathrm{Coexponential}(b,c) \sqcup \mathrm{Coexponential}(a,b).
‣ CocartesianPostCoComposeMorphism ( a, b, c ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( \mathrm{Coexponential}(a,c), \mathrm{Coexponential}(a,b) \sqcup \mathrm{Coexponential}(b,c) ).
The arguments are three objects a,b,c. The output is the postcocomposition morphism \mathrm{CocartesianPostCoComposeMorphism}_{a,b,c}: \mathrm{Coexponential}(a,c) \rightarrow \mathrm{Coexponential}(a,b) \sqcup \mathrm{Coexponential}(b,c).
‣ CocartesianPostCoComposeMorphismWithGivenObjects ( s, a, b, c, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( s, r ).
The arguments are an object s = \mathrm{Coexponential}(a,c), three objects a,b,c, and an object r = \mathrm{Coexponential}(b,c) \sqcup \mathrm{Coexponential}(a,b). The output is the postcocomposition morphism \mathrm{CocartesianPostCoComposeMorphismWithGivenObjects}_{a,b,c}: \mathrm{Coexponential}(a,c) \rightarrow \mathrm{Coexponential}(a,b) \sqcup \mathrm{Coexponential}(b,c).
‣ CocartesianDualOnObjects ( a ) | ( attribute ) |
Returns: an object
The argument is an object a. The output is its codual object a_{\vee}.
‣ CocartesianDualOnMorphisms ( alpha ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}( b_{\vee}, a_{\vee} ).
The argument is a morphism \alpha: a \rightarrow b. The output is its codual morphism \alpha_{\vee}: b_{\vee} \rightarrow a_{\vee}.
‣ CocartesianDualOnMorphismsWithGivenCocartesianDuals ( s, alpha, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( s, r ).
The argument is an object s = b_{\vee}, a morphism \alpha: a \rightarrow b, and an object r = a_{\vee}. The output is the dual morphism \alpha_{\vee}: b^{\vee} \rightarrow a^{\vee}.
‣ CocartesianEvaluationForCocartesianDual ( a ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}( 1, a_{\vee} \sqcup a ).
The argument is an object a. The output is the cocartesian evaluation morphism \mathrm{cocaev}_{a}: 1 \rightarrow a_{\vee} \sqcup a.
‣ CocartesianEvaluationForCocartesianDualWithGivenCoproduct ( s, a, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( s, r ).
The arguments are an object s = 1, an object a, and an object r = a_{\vee} \sqcup a. The output is the cocartesian evaluation morphism \mathrm{cocaev}_{a}: 1 \rightarrow a_{\vee} \sqcup a.
‣ MorphismFromCocartesianBidual ( a ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}((a_{\vee})_{\vee}, a).
The argument is an object a. The output is the morphism from the cobidual (a_{\vee})_{\vee} \rightarrow a.
‣ MorphismFromCocartesianBidualWithGivenCocartesianBidual ( a, s ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(s, a).
The arguments are an object a, and an object s = (a_{\vee})_{\vee}. The output is the morphism from the cobidual (a_{\vee})_{\vee} \rightarrow a.
‣ CoexponentialCoproductCompatibilityMorphism ( list ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( \mathrm{Coexponential}(a \sqcup a', b \sqcup b'), \mathrm{Coexponential}(a,b) \sqcup \mathrm{Coexponential}(a',b')).
The argument is a list of four objects [ a, a', b, b' ]. The output is the natural morphism \mathrm{CoexponentialCoproductCompatibilityMorphism}_{a,a',b,b'}: \mathrm{Coexponential}(a \sqcup a', b \sqcup b') \rightarrow \mathrm{Coexponential}(a,b) \sqcup \mathrm{Coexponential}(a',b').
‣ CoexponentialCoproductCompatibilityMorphismWithGivenObjects ( s, list, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( s, r ).
The arguments are a list of four objects [ a, a', b, b' ], and two objects s = \mathrm{Coexponential}(a \sqcup a', b \sqcup b') and r = \mathrm{Coexponential}(a,b) \sqcup \mathrm{Coexponential}(a',b'). The output is the natural morphism \mathrm{CoexponentialCoproductCompatibilityMorphismWithGivenObjects}_{a,a',b,b'}: \mathrm{Coexponential}(a \sqcup a', b \sqcup b') \rightarrow \mathrm{Coexponential}(a,b) \sqcup \mathrm{Coexponential}(a',b').
‣ CocartesianDualityCoproductCompatibilityMorphism ( a, b ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( (a \sqcup b)_{\vee}, a_{\vee} \sqcup b_{\vee} ).
The arguments are two objects a,b. The output is the natural morphism \mathrm{CocartesianDualityCoproductCompatibilityMorphism}: (a \sqcup b)_{\vee} \rightarrow a_{\vee} \sqcup b_{\vee}.
‣ CocartesianDualityCoproductCompatibilityMorphismWithGivenObjects ( s, a, b, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( s, r ).
The arguments are an object s = (a \sqcup b)_{\vee}, two objects a,b, and an object r = a_{\vee} \sqcup b_{\vee}. The output is the natural morphism \mathrm{CocartesianDualityCoproductCompatibilityMorphismWithGivenObjects}_{a,b}: (a \sqcup b)_{\vee} \rightarrow a_{\vee} \sqcup b_{\vee}.
‣ MorphismFromCoexponentialToCoproduct ( a, b ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( \mathrm{Coexponential}(a,b), b_{\vee} \sqcup a ).
The arguments are two objects a,b. The output is the natural morphism \mathrm{MorphismFromCoexponentialToCoproduct}_{a,b}: \mathrm{Coexponential}(a,b) \rightarrow b_{\vee} \sqcup a.
‣ MorphismFromCoexponentialToCoproductWithGivenObjects ( s, a, b, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( s, r ).
The arguments are an object s = \mathrm{Coexponential}(a,b), two objects a,b, and an object r = b_{\vee} \sqcup a. The output is the natural morphism \mathrm{MorphismFromCoexponentialToCoproductWithGivenObjects}_{a,b}: \mathrm{Coexponential}(a,b) \rightarrow a \sqcup b_{\vee}.
‣ IsomorphismFromCocartesianDualObjectToCoexponentialFromInitialObject ( a ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}(a_{\vee}, \mathrm{Coexponential}(1,a)).
The argument is an object a. The output is the isomorphism \mathrm{IsomorphismFromCocartesianDualObjectToCoexponentialFromInitialObject}_{a}: a_{\vee} \rightarrow \mathrm{Coexponential}(1,a).
‣ IsomorphismFromCoexponentialFromInitialObjectToCocartesianDualObject ( a ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}(\mathrm{Coexponential}(1,a), a_{\vee}).
The argument is an object a. The output is the isomorphism \mathrm{IsomorphismFromCoexponentialFromInitialObjectToCocartesianDualObject}_{a}: \mathrm{Coexponential}(1,a) \rightarrow a_{\vee}.
‣ UniversalPropertyOfCocartesianDual ( t, a, alpha ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(a_{\vee}, t).
The arguments are two objects t,a, and a morphism \alpha: 1 \rightarrow t \sqcup a. The output is the morphism a_{\vee} \rightarrow t given by the universal property of a_{\vee}.
‣ CocartesianLambdaIntroduction ( alpha ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}( \mathrm{Coexponential}(a,b), 1 ).
The argument is a morphism \alpha: a \rightarrow b. The output is the corresponding morphism \mathrm{Coexponential}(a,b) \rightarrow 1 under the coexponential-coproduct adjunction.
‣ CocartesianLambdaElimination ( a, b, alpha ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(a,b).
The arguments are two objects a,b, and a morphism \alpha: \mathrm{Coexponential}(a,b) \rightarrow 1. The output is a morphism a \rightarrow b corresponding to \alpha under the coexponential-coproduct adjunction.
‣ IsomorphismFromObjectToCoexponential ( a ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}(a, \mathrm{Coexponential}(a,1)).
The argument is an object a. The output is the natural isomorphism a \rightarrow \mathrm{Coexponential}(a,1).
‣ IsomorphismFromObjectToCoexponentialWithGivenCoexponential ( a, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(a, r).
The argument is an object a, and an object r = \mathrm{Coexponential}(a,1). The output is the natural isomorphism a \rightarrow \mathrm{Coexponential}(a,1).
‣ IsomorphismFromCoexponentialToObject ( a ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}(\mathrm{Coexponential}(a,1), a).
The argument is an object a. The output is the natural isomorphism \mathrm{Coexponential}(a,1) \rightarrow a.
‣ IsomorphismFromCoexponentialToObjectWithGivenCoexponential ( a, s ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(s, a).
The argument is an object a, and an object s = \mathrm{Coexponential}(a,1). The output is the natural isomorphism \mathrm{Coexponential}(a,1) \rightarrow a.
‣ Coexponential ( a, b ) | ( operation ) |
Returns: a cell
This is a convenience method. The arguments are two cells a,b. The output is the coexponential cell. If a,b are two CAP objects the output is the coexponential object \mathrm{Coexponential}(a,b). If at least one of the arguments is a CAP morphism the output is a CAP morphism, namely the coexponential on morphisms, where any object is replaced by its identity morphism.
‣ AddCocartesianBraiding ( C, F ) | ( operation ) |
‣ AddCocartesianBraiding ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianBraiding
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b ) \mapsto \mathtt{CocartesianBraiding}(a, b).
‣ AddCocartesianBraidingInverse ( C, F ) | ( operation ) |
‣ AddCocartesianBraidingInverse ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianBraidingInverse
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b ) \mapsto \mathtt{CocartesianBraidingInverse}(a, b).
‣ AddCocartesianBraidingInverseWithGivenCoproducts ( C, F ) | ( operation ) |
‣ AddCocartesianBraidingInverseWithGivenCoproducts ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianBraidingInverseWithGivenCoproducts
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, a, b, r ) \mapsto \mathtt{CocartesianBraidingInverseWithGivenCoproducts}(s, a, b, r).
‣ AddCocartesianBraidingWithGivenCoproducts ( C, F ) | ( operation ) |
‣ AddCocartesianBraidingWithGivenCoproducts ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianBraidingWithGivenCoproducts
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, a, b, r ) \mapsto \mathtt{CocartesianBraidingWithGivenCoproducts}(s, a, b, r).
‣ AddCocartesianAssociatorLeftToRight ( C, F ) | ( operation ) |
‣ AddCocartesianAssociatorLeftToRight ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianAssociatorLeftToRight
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b, c ) \mapsto \mathtt{CocartesianAssociatorLeftToRight}(a, b, c).
‣ AddCocartesianAssociatorLeftToRightWithGivenCoproducts ( C, F ) | ( operation ) |
‣ AddCocartesianAssociatorLeftToRightWithGivenCoproducts ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianAssociatorLeftToRightWithGivenCoproducts
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, a, b, c, r ) \mapsto \mathtt{CocartesianAssociatorLeftToRightWithGivenCoproducts}(s, a, b, c, r).
‣ AddCocartesianAssociatorRightToLeft ( C, F ) | ( operation ) |
‣ AddCocartesianAssociatorRightToLeft ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianAssociatorRightToLeft
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b, c ) \mapsto \mathtt{CocartesianAssociatorRightToLeft}(a, b, c).
‣ AddCocartesianAssociatorRightToLeftWithGivenCoproducts ( C, F ) | ( operation ) |
‣ AddCocartesianAssociatorRightToLeftWithGivenCoproducts ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianAssociatorRightToLeftWithGivenCoproducts
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, a, b, c, r ) \mapsto \mathtt{CocartesianAssociatorRightToLeftWithGivenCoproducts}(s, a, b, c, r).
‣ AddCocartesianCodiagonal ( C, F ) | ( operation ) |
‣ AddCocartesianCodiagonal ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianCodiagonal
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, n ) \mapsto \mathtt{CocartesianCodiagonal}(a, n).
‣ AddCocartesianCodiagonalWithGivenCocartesianMultiple ( C, F ) | ( operation ) |
‣ AddCocartesianCodiagonalWithGivenCocartesianMultiple ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianCodiagonalWithGivenCocartesianMultiple
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, n, cocartesian_multiple ) \mapsto \mathtt{CocartesianCodiagonalWithGivenCocartesianMultiple}(a, n, cocartesian_multiple).
‣ AddCocartesianLeftUnitor ( C, F ) | ( operation ) |
‣ AddCocartesianLeftUnitor ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianLeftUnitor
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a ) \mapsto \mathtt{CocartesianLeftUnitor}(a).
‣ AddCocartesianLeftUnitorInverse ( C, F ) | ( operation ) |
‣ AddCocartesianLeftUnitorInverse ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianLeftUnitorInverse
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a ) \mapsto \mathtt{CocartesianLeftUnitorInverse}(a).
‣ AddCocartesianLeftUnitorInverseWithGivenCoproduct ( C, F ) | ( operation ) |
‣ AddCocartesianLeftUnitorInverseWithGivenCoproduct ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianLeftUnitorInverseWithGivenCoproduct
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, r ) \mapsto \mathtt{CocartesianLeftUnitorInverseWithGivenCoproduct}(a, r).
‣ AddCocartesianLeftUnitorWithGivenCoproduct ( C, F ) | ( operation ) |
‣ AddCocartesianLeftUnitorWithGivenCoproduct ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianLeftUnitorWithGivenCoproduct
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, s ) \mapsto \mathtt{CocartesianLeftUnitorWithGivenCoproduct}(a, s).
‣ AddCocartesianRightUnitor ( C, F ) | ( operation ) |
‣ AddCocartesianRightUnitor ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianRightUnitor
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a ) \mapsto \mathtt{CocartesianRightUnitor}(a).
‣ AddCocartesianRightUnitorInverse ( C, F ) | ( operation ) |
‣ AddCocartesianRightUnitorInverse ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianRightUnitorInverse
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a ) \mapsto \mathtt{CocartesianRightUnitorInverse}(a).
‣ AddCocartesianRightUnitorInverseWithGivenCoproduct ( C, F ) | ( operation ) |
‣ AddCocartesianRightUnitorInverseWithGivenCoproduct ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianRightUnitorInverseWithGivenCoproduct
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, r ) \mapsto \mathtt{CocartesianRightUnitorInverseWithGivenCoproduct}(a, r).
‣ AddCocartesianRightUnitorWithGivenCoproduct ( C, F ) | ( operation ) |
‣ AddCocartesianRightUnitorWithGivenCoproduct ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianRightUnitorWithGivenCoproduct
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, s ) \mapsto \mathtt{CocartesianRightUnitorWithGivenCoproduct}(a, s).
‣ AddCoproductOnMorphisms ( C, F ) | ( operation ) |
‣ AddCoproductOnMorphisms ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoproductOnMorphisms
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( alpha, beta ) \mapsto \mathtt{CoproductOnMorphisms}(alpha, beta).
‣ AddCoproductOnMorphismsWithGivenCoproducts ( C, F ) | ( operation ) |
‣ AddCoproductOnMorphismsWithGivenCoproducts ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoproductOnMorphismsWithGivenCoproducts
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, alpha, beta, r ) \mapsto \mathtt{CoproductOnMorphismsWithGivenCoproducts}(s, alpha, beta, r).
‣ AddCocartesianDualOnMorphisms ( C, F ) | ( operation ) |
‣ AddCocartesianDualOnMorphisms ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianDualOnMorphisms
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( alpha ) \mapsto \mathtt{CocartesianDualOnMorphisms}(alpha).
‣ AddCocartesianDualOnMorphismsWithGivenCocartesianDuals ( C, F ) | ( operation ) |
‣ AddCocartesianDualOnMorphismsWithGivenCocartesianDuals ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianDualOnMorphismsWithGivenCocartesianDuals
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, alpha, r ) \mapsto \mathtt{CocartesianDualOnMorphismsWithGivenCocartesianDuals}(s, alpha, r).
‣ AddCocartesianDualOnObjects ( C, F ) | ( operation ) |
‣ AddCocartesianDualOnObjects ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianDualOnObjects
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a ) \mapsto \mathtt{CocartesianDualOnObjects}(a).
‣ AddCocartesianDualityCoproductCompatibilityMorphism ( C, F ) | ( operation ) |
‣ AddCocartesianDualityCoproductCompatibilityMorphism ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianDualityCoproductCompatibilityMorphism
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b ) \mapsto \mathtt{CocartesianDualityCoproductCompatibilityMorphism}(a, b).
‣ AddCocartesianDualityCoproductCompatibilityMorphismWithGivenObjects ( C, F ) | ( operation ) |
‣ AddCocartesianDualityCoproductCompatibilityMorphismWithGivenObjects ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianDualityCoproductCompatibilityMorphismWithGivenObjects
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, a, b, r ) \mapsto \mathtt{CocartesianDualityCoproductCompatibilityMorphismWithGivenObjects}(s, a, b, r).
‣ AddCocartesianEvaluationForCocartesianDual ( C, F ) | ( operation ) |
‣ AddCocartesianEvaluationForCocartesianDual ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianEvaluationForCocartesianDual
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a ) \mapsto \mathtt{CocartesianEvaluationForCocartesianDual}(a).
‣ AddCocartesianEvaluationForCocartesianDualWithGivenCoproduct ( C, F ) | ( operation ) |
‣ AddCocartesianEvaluationForCocartesianDualWithGivenCoproduct ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianEvaluationForCocartesianDualWithGivenCoproduct
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, a, r ) \mapsto \mathtt{CocartesianEvaluationForCocartesianDualWithGivenCoproduct}(s, a, r).
‣ AddCocartesianLambdaElimination ( C, F ) | ( operation ) |
‣ AddCocartesianLambdaElimination ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianLambdaElimination
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b, alpha ) \mapsto \mathtt{CocartesianLambdaElimination}(a, b, alpha).
‣ AddCocartesianLambdaIntroduction ( C, F ) | ( operation ) |
‣ AddCocartesianLambdaIntroduction ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianLambdaIntroduction
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( alpha ) \mapsto \mathtt{CocartesianLambdaIntroduction}(alpha).
‣ AddCocartesianLeftCoevaluationMorphism ( C, F ) | ( operation ) |
‣ AddCocartesianLeftCoevaluationMorphism ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianLeftCoevaluationMorphism
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b ) \mapsto \mathtt{CocartesianLeftCoevaluationMorphism}(a, b).
‣ AddCocartesianLeftCoevaluationMorphismWithGivenSource ( C, F ) | ( operation ) |
‣ AddCocartesianLeftCoevaluationMorphismWithGivenSource ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianLeftCoevaluationMorphismWithGivenSource
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b, s ) \mapsto \mathtt{CocartesianLeftCoevaluationMorphismWithGivenSource}(a, b, s).
‣ AddCocartesianLeftEvaluationMorphism ( C, F ) | ( operation ) |
‣ AddCocartesianLeftEvaluationMorphism ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianLeftEvaluationMorphism
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b ) \mapsto \mathtt{CocartesianLeftEvaluationMorphism}(a, b).
‣ AddCocartesianLeftEvaluationMorphismWithGivenRange ( C, F ) | ( operation ) |
‣ AddCocartesianLeftEvaluationMorphismWithGivenRange ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianLeftEvaluationMorphismWithGivenRange
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b, r ) \mapsto \mathtt{CocartesianLeftEvaluationMorphismWithGivenRange}(a, b, r).
‣ AddCocartesianPostCoComposeMorphism ( C, F ) | ( operation ) |
‣ AddCocartesianPostCoComposeMorphism ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianPostCoComposeMorphism
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b, c ) \mapsto \mathtt{CocartesianPostCoComposeMorphism}(a, b, c).
‣ AddCocartesianPostCoComposeMorphismWithGivenObjects ( C, F ) | ( operation ) |
‣ AddCocartesianPostCoComposeMorphismWithGivenObjects ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianPostCoComposeMorphismWithGivenObjects
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, a, b, c, r ) \mapsto \mathtt{CocartesianPostCoComposeMorphismWithGivenObjects}(s, a, b, c, r).
‣ AddCocartesianPreCoComposeMorphism ( C, F ) | ( operation ) |
‣ AddCocartesianPreCoComposeMorphism ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianPreCoComposeMorphism
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b, c ) \mapsto \mathtt{CocartesianPreCoComposeMorphism}(a, b, c).
‣ AddCocartesianPreCoComposeMorphismWithGivenObjects ( C, F ) | ( operation ) |
‣ AddCocartesianPreCoComposeMorphismWithGivenObjects ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianPreCoComposeMorphismWithGivenObjects
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, a, b, c, r ) \mapsto \mathtt{CocartesianPreCoComposeMorphismWithGivenObjects}(s, a, b, c, r).
‣ AddCocartesianRightCoevaluationMorphism ( C, F ) | ( operation ) |
‣ AddCocartesianRightCoevaluationMorphism ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianRightCoevaluationMorphism
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b ) \mapsto \mathtt{CocartesianRightCoevaluationMorphism}(a, b).
‣ AddCocartesianRightCoevaluationMorphismWithGivenSource ( C, F ) | ( operation ) |
‣ AddCocartesianRightCoevaluationMorphismWithGivenSource ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianRightCoevaluationMorphismWithGivenSource
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b, s ) \mapsto \mathtt{CocartesianRightCoevaluationMorphismWithGivenSource}(a, b, s).
‣ AddCocartesianRightEvaluationMorphism ( C, F ) | ( operation ) |
‣ AddCocartesianRightEvaluationMorphism ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianRightEvaluationMorphism
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b ) \mapsto \mathtt{CocartesianRightEvaluationMorphism}(a, b).
‣ AddCocartesianRightEvaluationMorphismWithGivenRange ( C, F ) | ( operation ) |
‣ AddCocartesianRightEvaluationMorphismWithGivenRange ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CocartesianRightEvaluationMorphismWithGivenRange
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b, r ) \mapsto \mathtt{CocartesianRightEvaluationMorphismWithGivenRange}(a, b, r).
‣ AddCoexponentialCoproductCompatibilityMorphism ( C, F ) | ( operation ) |
‣ AddCoexponentialCoproductCompatibilityMorphism ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoexponentialCoproductCompatibilityMorphism
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( list ) \mapsto \mathtt{CoexponentialCoproductCompatibilityMorphism}(list).
‣ AddCoexponentialCoproductCompatibilityMorphismWithGivenObjects ( C, F ) | ( operation ) |
‣ AddCoexponentialCoproductCompatibilityMorphismWithGivenObjects ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoexponentialCoproductCompatibilityMorphismWithGivenObjects
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( source, list, range ) \mapsto \mathtt{CoexponentialCoproductCompatibilityMorphismWithGivenObjects}(source, list, range).
‣ AddCoexponentialOnMorphisms ( C, F ) | ( operation ) |
‣ AddCoexponentialOnMorphisms ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoexponentialOnMorphisms
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( alpha, beta ) \mapsto \mathtt{CoexponentialOnMorphisms}(alpha, beta).
‣ AddCoexponentialOnMorphismsWithGivenCoexponentials ( C, F ) | ( operation ) |
‣ AddCoexponentialOnMorphismsWithGivenCoexponentials ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoexponentialOnMorphismsWithGivenCoexponentials
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, alpha, beta, r ) \mapsto \mathtt{CoexponentialOnMorphismsWithGivenCoexponentials}(s, alpha, beta, r).
‣ AddCoexponentialOnObjects ( C, F ) | ( operation ) |
‣ AddCoexponentialOnObjects ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoexponentialOnObjects
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b ) \mapsto \mathtt{CoexponentialOnObjects}(a, b).
‣ AddCoexponentialToCoproductLeftAdjunctMorphism ( C, F ) | ( operation ) |
‣ AddCoexponentialToCoproductLeftAdjunctMorphism ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoexponentialToCoproductLeftAdjunctMorphism
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, c, f ) \mapsto \mathtt{CoexponentialToCoproductLeftAdjunctMorphism}(a, c, f).
‣ AddCoexponentialToCoproductLeftAdjunctMorphismWithGivenCoproduct ( C, F ) | ( operation ) |
‣ AddCoexponentialToCoproductLeftAdjunctMorphismWithGivenCoproduct ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoexponentialToCoproductLeftAdjunctMorphismWithGivenCoproduct
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, c, f, t ) \mapsto \mathtt{CoexponentialToCoproductLeftAdjunctMorphismWithGivenCoproduct}(a, c, f, t).
‣ AddCoexponentialToCoproductRightAdjunctMorphism ( C, F ) | ( operation ) |
‣ AddCoexponentialToCoproductRightAdjunctMorphism ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoexponentialToCoproductRightAdjunctMorphism
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b, f ) \mapsto \mathtt{CoexponentialToCoproductRightAdjunctMorphism}(a, b, f).
‣ AddCoexponentialToCoproductRightAdjunctMorphismWithGivenCoproduct ( C, F ) | ( operation ) |
‣ AddCoexponentialToCoproductRightAdjunctMorphismWithGivenCoproduct ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoexponentialToCoproductRightAdjunctMorphismWithGivenCoproduct
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b, f, t ) \mapsto \mathtt{CoexponentialToCoproductRightAdjunctMorphismWithGivenCoproduct}(a, b, f, t).
‣ AddCoproductToCoexponentialLeftAdjunctMorphism ( C, F ) | ( operation ) |
‣ AddCoproductToCoexponentialLeftAdjunctMorphism ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoproductToCoexponentialLeftAdjunctMorphism
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( b, c, g ) \mapsto \mathtt{CoproductToCoexponentialLeftAdjunctMorphism}(b, c, g).
‣ AddCoproductToCoexponentialLeftAdjunctMorphismWithGivenCoexponential ( C, F ) | ( operation ) |
‣ AddCoproductToCoexponentialLeftAdjunctMorphismWithGivenCoexponential ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoproductToCoexponentialLeftAdjunctMorphismWithGivenCoexponential
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( b, c, g, i ) \mapsto \mathtt{CoproductToCoexponentialLeftAdjunctMorphismWithGivenCoexponential}(b, c, g, i).
‣ AddCoproductToCoexponentialRightAdjunctMorphism ( C, F ) | ( operation ) |
‣ AddCoproductToCoexponentialRightAdjunctMorphism ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoproductToCoexponentialRightAdjunctMorphism
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( b, c, g ) \mapsto \mathtt{CoproductToCoexponentialRightAdjunctMorphism}(b, c, g).
‣ AddCoproductToCoexponentialRightAdjunctMorphismWithGivenCoexponential ( C, F ) | ( operation ) |
‣ AddCoproductToCoexponentialRightAdjunctMorphismWithGivenCoexponential ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation CoproductToCoexponentialRightAdjunctMorphismWithGivenCoexponential
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( b, c, g, i ) \mapsto \mathtt{CoproductToCoexponentialRightAdjunctMorphismWithGivenCoexponential}(b, c, g, i).
‣ AddIsomorphismFromCocartesianDualObjectToCoexponentialFromInitialObject ( C, F ) | ( operation ) |
‣ AddIsomorphismFromCocartesianDualObjectToCoexponentialFromInitialObject ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation IsomorphismFromCocartesianDualObjectToCoexponentialFromInitialObject
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a ) \mapsto \mathtt{IsomorphismFromCocartesianDualObjectToCoexponentialFromInitialObject}(a).
‣ AddIsomorphismFromCoexponentialFromInitialObjectToCocartesianDualObject ( C, F ) | ( operation ) |
‣ AddIsomorphismFromCoexponentialFromInitialObjectToCocartesianDualObject ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation IsomorphismFromCoexponentialFromInitialObjectToCocartesianDualObject
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a ) \mapsto \mathtt{IsomorphismFromCoexponentialFromInitialObjectToCocartesianDualObject}(a).
‣ AddIsomorphismFromCoexponentialToObject ( C, F ) | ( operation ) |
‣ AddIsomorphismFromCoexponentialToObject ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation IsomorphismFromCoexponentialToObject
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a ) \mapsto \mathtt{IsomorphismFromCoexponentialToObject}(a).
‣ AddIsomorphismFromCoexponentialToObjectWithGivenCoexponential ( C, F ) | ( operation ) |
‣ AddIsomorphismFromCoexponentialToObjectWithGivenCoexponential ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation IsomorphismFromCoexponentialToObjectWithGivenCoexponential
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, s ) \mapsto \mathtt{IsomorphismFromCoexponentialToObjectWithGivenCoexponential}(a, s).
‣ AddIsomorphismFromObjectToCoexponential ( C, F ) | ( operation ) |
‣ AddIsomorphismFromObjectToCoexponential ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation IsomorphismFromObjectToCoexponential
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a ) \mapsto \mathtt{IsomorphismFromObjectToCoexponential}(a).
‣ AddIsomorphismFromObjectToCoexponentialWithGivenCoexponential ( C, F ) | ( operation ) |
‣ AddIsomorphismFromObjectToCoexponentialWithGivenCoexponential ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation IsomorphismFromObjectToCoexponentialWithGivenCoexponential
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, r ) \mapsto \mathtt{IsomorphismFromObjectToCoexponentialWithGivenCoexponential}(a, r).
‣ AddMorphismFromCocartesianBidual ( C, F ) | ( operation ) |
‣ AddMorphismFromCocartesianBidual ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation MorphismFromCocartesianBidual
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a ) \mapsto \mathtt{MorphismFromCocartesianBidual}(a).
‣ AddMorphismFromCocartesianBidualWithGivenCocartesianBidual ( C, F ) | ( operation ) |
‣ AddMorphismFromCocartesianBidualWithGivenCocartesianBidual ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation MorphismFromCocartesianBidualWithGivenCocartesianBidual
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, s ) \mapsto \mathtt{MorphismFromCocartesianBidualWithGivenCocartesianBidual}(a, s).
‣ AddMorphismFromCoexponentialToCoproduct ( C, F ) | ( operation ) |
‣ AddMorphismFromCoexponentialToCoproduct ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation MorphismFromCoexponentialToCoproduct
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, b ) \mapsto \mathtt{MorphismFromCoexponentialToCoproduct}(a, b).
‣ AddMorphismFromCoexponentialToCoproductWithGivenObjects ( C, F ) | ( operation ) |
‣ AddMorphismFromCoexponentialToCoproductWithGivenObjects ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation MorphismFromCoexponentialToCoproductWithGivenObjects
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, a, b, r ) \mapsto \mathtt{MorphismFromCoexponentialToCoproductWithGivenObjects}(s, a, b, r).
‣ AddUniversalPropertyOfCocartesianDual ( C, F ) | ( operation ) |
‣ AddUniversalPropertyOfCocartesianDual ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation UniversalPropertyOfCocartesianDual
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( t, a, alpha ) \mapsto \mathtt{UniversalPropertyOfCocartesianDual}(t, a, alpha).
‣ AddLeftCocartesianCodistributivityExpanding ( C, F ) | ( operation ) |
‣ AddLeftCocartesianCodistributivityExpanding ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation LeftCocartesianCodistributivityExpanding
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, L ) \mapsto \mathtt{LeftCocartesianCodistributivityExpanding}(a, L).
‣ AddLeftCocartesianCodistributivityExpandingWithGivenObjects ( C, F ) | ( operation ) |
‣ AddLeftCocartesianCodistributivityExpandingWithGivenObjects ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation LeftCocartesianCodistributivityExpandingWithGivenObjects
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, a, L, r ) \mapsto \mathtt{LeftCocartesianCodistributivityExpandingWithGivenObjects}(s, a, L, r).
‣ AddLeftCocartesianCodistributivityFactoring ( C, F ) | ( operation ) |
‣ AddLeftCocartesianCodistributivityFactoring ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation LeftCocartesianCodistributivityFactoring
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( a, L ) \mapsto \mathtt{LeftCocartesianCodistributivityFactoring}(a, L).
‣ AddLeftCocartesianCodistributivityFactoringWithGivenObjects ( C, F ) | ( operation ) |
‣ AddLeftCocartesianCodistributivityFactoringWithGivenObjects ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation LeftCocartesianCodistributivityFactoringWithGivenObjects
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, a, L, r ) \mapsto \mathtt{LeftCocartesianCodistributivityFactoringWithGivenObjects}(s, a, L, r).
‣ AddRightCocartesianCodistributivityExpanding ( C, F ) | ( operation ) |
‣ AddRightCocartesianCodistributivityExpanding ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation RightCocartesianCodistributivityExpanding
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( L, a ) \mapsto \mathtt{RightCocartesianCodistributivityExpanding}(L, a).
‣ AddRightCocartesianCodistributivityExpandingWithGivenObjects ( C, F ) | ( operation ) |
‣ AddRightCocartesianCodistributivityExpandingWithGivenObjects ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation RightCocartesianCodistributivityExpandingWithGivenObjects
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, L, a, r ) \mapsto \mathtt{RightCocartesianCodistributivityExpandingWithGivenObjects}(s, L, a, r).
‣ AddRightCocartesianCodistributivityFactoring ( C, F ) | ( operation ) |
‣ AddRightCocartesianCodistributivityFactoring ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation RightCocartesianCodistributivityFactoring
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( L, a ) \mapsto \mathtt{RightCocartesianCodistributivityFactoring}(L, a).
‣ AddRightCocartesianCodistributivityFactoringWithGivenObjects ( C, F ) | ( operation ) |
‣ AddRightCocartesianCodistributivityFactoringWithGivenObjects ( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category C and a function F. This operation adds the given function F to the category for the basic operation RightCocartesianCodistributivityFactoringWithGivenObjects
. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). F: ( s, L, a, r ) \mapsto \mathtt{RightCocartesianCodistributivityFactoringWithGivenObjects}(s, L, a, r).
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