‣ 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.
‣ 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 ) |
‣ AddConegationOnMorphisms( 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 ConegationOnMorphisms. 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). \(F: ( alpha ) \mapsto \mathtt{ConegationOnMorphisms}(alpha)\).
‣ AddConegationOnMorphismsWithGivenConegations( C, F ) | ( operation ) |
‣ AddConegationOnMorphismsWithGivenConegations( 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 ConegationOnMorphismsWithGivenConegations. 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). \(F: ( s, alpha, r ) \mapsto \mathtt{ConegationOnMorphismsWithGivenConegations}(s, alpha, r)\).
‣ AddConegationOnObjects( C, F ) | ( operation ) |
‣ AddConegationOnObjects( 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 ConegationOnObjects. 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). \(F: ( arg2 ) \mapsto \mathtt{ConegationOnObjects}(arg2)\).
‣ AddMorphismFromDoubleConegation( C, F ) | ( operation ) |
‣ AddMorphismFromDoubleConegation( 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 MorphismFromDoubleConegation. 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). \(F: ( a ) \mapsto \mathtt{MorphismFromDoubleConegation}(a)\).
‣ AddMorphismFromDoubleConegationWithGivenDoubleConegation( C, F ) | ( operation ) |
‣ AddMorphismFromDoubleConegationWithGivenDoubleConegation( 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 MorphismFromDoubleConegationWithGivenDoubleConegation. 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). \(F: ( a, s ) \mapsto \mathtt{MorphismFromDoubleConegationWithGivenDoubleConegation}(a, s)\).
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