‣ 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.
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