‣ ConegationOnObjects( a ) | ( attribute ) |
Returns: an object
The argument is an object a. The output is its co-negated object \ulcorner a.
‣ ConegationOnMorphisms( alpha ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}( \ulcorner b, \ulcorner a ).
The argument is a morphism \alpha: a \rightarrow b. The output is its negated morphism \ulcorner \alpha: \ulcorner b \rightarrow \ulcorner a.
‣ ConegationOnMorphismsWithGivenConegations( s, alpha, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}( \ulcorner b, \ulcorner a ).
The argument is an object s = \ulcorner b, a morphism \alpha: a \rightarrow b, and an object r = \ulcorner a. The output is the negated morphism \ulcorner \alpha: \ulcorner b \rightarrow \ulcorner a.
‣ MorphismFromDoubleConegation( a ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}(\ulcorner\ulcorner a, a).
The argument is an object a. The output is the morphism from the double conegation \ulcorner\ulcorner a \rightarrow a.
‣ MorphismFromDoubleConegationWithGivenDoubleConegation( a, r ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(\ulcorner\ulcorner a, a).
The arguments are an object a, and an object r = \ulcorner\ulcorner a. The output is the morphism from the double conegation \ulcorner\ulcorner a \rightarrow a.
‣ StableInternalCoHom( V, W ) | ( operation ) |
Returns: a CAP object
Return the stable internal coHom: \mathrm{\underline{coHom}}(\mathrm{\underline{coHom}}(...\mathrm{\underline{coHom}}(V,W)...,W),W).
‣ AddConegationOnMorphisms( C, F ) | ( 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 ConegationOnMorphisms. F: ( alpha ) \mapsto \mathtt{ConegationOnMorphisms}(alpha).
‣ AddConegationOnMorphismsWithGivenConegations( C, F ) | ( 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 ConegationOnMorphismsWithGivenConegations. F: ( s, alpha, r ) \mapsto \mathtt{ConegationOnMorphismsWithGivenConegations}(s, alpha, r).
‣ AddConegationOnObjects( C, F ) | ( 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 ConegationOnObjects. F: ( arg2 ) \mapsto \mathtt{ConegationOnObjects}(arg2).
‣ AddMorphismFromDoubleConegation( C, F ) | ( 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 MorphismFromDoubleConegation. F: ( a ) \mapsto \mathtt{MorphismFromDoubleConegation}(a).
‣ AddMorphismFromDoubleConegationWithGivenDoubleConegation( C, F ) | ( 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 MorphismFromDoubleConegationWithGivenDoubleConegation. F: ( a, s ) \mapsto \mathtt{MorphismFromDoubleConegationWithGivenDoubleConegation}(a, s).
‣ IsCoHeytingAlgebroid( C ) | ( property ) |
Returns: true or false
The property of C being a co-Heyting algebroid.
‣ IsCoHeytingAlgebra( C ) | ( property ) |
Returns: true or false
The property of C being a co-Heyting algebra.
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