‣ IsQuotientCategory ( C ) | ( filter ) |
Returns: a boolian
The Gap filter of the Cap quotient categories.
‣ IsQuotientCategoryMorphism ( alpha ) | ( filter ) |
Returns: a boolian
The gap category of quotient categories morphisms
‣ IsQuotientCategoryCell ( a, object ) | ( filter ) |
Returns: true
or false
The GAP category of cells in the quotient category.
‣ IsQuotientCategoryObject ( a, object ) | ( filter ) |
Returns: true
or false
The GAP category of objects in the quotient category.
‣ QuotientCategory ( C, F ) | ( operation ) |
Returns: a Cap category
The input is a category C and a function F. For two objects a and b in C, the function F can be applied on two morphisms \alpha,\beta \in \mathrm{Hom}_C(a,b) and returns true
if \alpha \sim \beta and false
otherwise. The output is the quotient category C/F.
‣ QuotientCategoryMorphism ( _a_, alpha, _b_ ) | ( operation ) |
Returns: a morphism
The arguments are two objects \underline{a}, \underline{b} in a quotient category Q=C/F and a morphism \alpha:a \rightarrow b in C. The output is \underline{\alpha}: \underline{a} \rightarrow \underline{b} in Q.
‣ QuotientCategoryMorphism ( Q, alpha ) | ( operation ) |
Returns: a morphism
The input is a quotient category Q=C/F and a morphism \alpha:a \rightarrow b in C. The output is \underline{\alpha}: \underline{a} \rightarrow \underline{b} in Q.
1.2-4 \/
‣ \/ ( Q, alpha ) | ( operation ) |
Returns: a morphism
The input is a quotient category Q=C/F and a morphism \alpha:a \rightarrow b in C. The output is \underline{\alpha}: \underline{a} \rightarrow \underline{b} in Q.
‣ QuotientCategoryObject ( Q, a ) | ( operation ) |
Returns: an object
The input is a quotient category Q=C/F and an object a \in C. The output is \underline{a} \in Q.
1.2-6 \/
‣ \/ ( a, Q ) | ( operation ) |
Returns: an object
The input is a quotient category Q=C/F and an object a \in C. The output is \underline{a} \in Q.
‣ UnderlyingCategory ( Q ) | ( attribute ) |
Returns: a category
The input is a quotient category Q := C/F. The output is the category C.
‣ CongruencyTestFunctionForQuotientCategory ( Q ) | ( attribute ) |
Returns: a function
The input is a quotient category Q := C/F. The output is the congruence test function F.
‣ ProjectionFunctor ( Q ) | ( attribute ) |
Returns: a functor
The input is a quotient category Q := C/F. The output is the canonical projection functor \pi:C \rightarrow C/F.
‣ UnderlyingCell ( _alpha_ ) | ( attribute ) |
Returns: a morphism
The input is a morphism \underline{\alpha}: \underline{a} \rightarrow \underline{b} in some quotient category Q=C/F and the output is \alpha: a \rightarrow b in C.
‣ UnderlyingCell ( _a_ ) | ( attribute ) |
Returns: an object
The input is an object \underline{a} in some quotient category Q=C/F and the output is a in C.
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