‣ IsHeytingAlgebroid( C ) | ( property ) |
Returns: true or false
The property of C being a Heyting algebroid.
‣ IsHeytingAlgebra( C ) | ( property ) |
Returns: true or false
The property of C being a Heyting algebra.
‣ NegationOnObjects( a ) | ( attribute ) |
Returns: an object
The argument is an object a. The output is its negated object \neg a.
‣ NegationOnMorphisms( alpha ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}( \neg b, \neg a ).
The argument is a morphism \alpha: a \rightarrow b. The output is its negated morphism \neg \alpha: \neg b \rightarrow \neg a.
‣ NegationOnMorphismsWithGivenNegations( s, alpha, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( \neg b, \neg a ).
The argument is an object s = \neg b, a morphism \alpha: a \rightarrow b, and an object r = \neg a. The output is the negated morphism \neg \alpha: \neg b \rightarrow \neg a.
‣ MorphismToDoubleNegation( a ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}(a, \neg\neg a).
The argument is an object a. The output is the morphism to the double negation a \rightarrow \neg\neg a.
‣ MorphismToDoubleNegationWithGivenDoubleNegation( a, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(a, \neg\neg a).
The arguments are an object a, and an object r = \neg\neg a. The output is the morphism to the double negation a \rightarrow \neg\neg a.
‣ StableInternalHom( J, I ) | ( operation ) |
Returns: a CAP object
Return the stable internal Hom: \mathrm{\underline{Hom}}(J,\mathrm{\underline{Hom}}(J,...\mathrm{\underline{Hom}}(J,I)...)).
‣ AddMorphismToDoubleNegation( C, F ) | ( operation ) |
‣ AddMorphismToDoubleNegation( 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 MorphismToDoubleNegation. 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{MorphismToDoubleNegation}(a).
‣ AddMorphismToDoubleNegationWithGivenDoubleNegation( C, F ) | ( operation ) |
‣ AddMorphismToDoubleNegationWithGivenDoubleNegation( 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 MorphismToDoubleNegationWithGivenDoubleNegation. 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{MorphismToDoubleNegationWithGivenDoubleNegation}(a, r).
‣ AddNegationOnMorphisms( C, F ) | ( operation ) |
‣ AddNegationOnMorphisms( 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 NegationOnMorphisms. 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{NegationOnMorphisms}(alpha).
‣ AddNegationOnMorphismsWithGivenNegations( C, F ) | ( operation ) |
‣ AddNegationOnMorphismsWithGivenNegations( 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 NegationOnMorphismsWithGivenNegations. 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{NegationOnMorphismsWithGivenNegations}(s, alpha, r).
‣ AddNegationOnObjects( C, F ) | ( operation ) |
‣ AddNegationOnObjects( 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 NegationOnObjects. 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: ( arg2 ) \mapsto \mathtt{NegationOnObjects}(arg2).
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