‣ 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 ) |
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. \(F: ( a ) \mapsto \mathtt{MorphismToDoubleNegation}(a)\).
‣ AddMorphismToDoubleNegationWithGivenDoubleNegation( 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 MorphismToDoubleNegationWithGivenDoubleNegation. \(F: ( a, r ) \mapsto \mathtt{MorphismToDoubleNegationWithGivenDoubleNegation}(a, r)\).
‣ AddNegationOnMorphisms( 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 NegationOnMorphisms. \(F: ( alpha ) \mapsto \mathtt{NegationOnMorphisms}(alpha)\).
‣ AddNegationOnMorphismsWithGivenNegations( 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 NegationOnMorphismsWithGivenNegations. \(F: ( s, alpha, r ) \mapsto \mathtt{NegationOnMorphismsWithGivenNegations}(s, alpha, r)\).
‣ AddNegationOnObjects( 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 NegationOnObjects. \(F: ( arg2 ) \mapsto \mathtt{NegationOnObjects}(arg2)\).
‣ 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.
generated by GAPDoc2HTML