‣ 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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