‣ IsChainOrCochainComplexCategory( arg ) | ( filter ) |
Returns: true or false
Gap-categories of the chain or cochain complexes category.
‣ IsBoundedChainOrCochainComplexCategory( arg ) | ( filter ) |
Returns: true or false
Gap-categories of the chain or cochain complexes category.
‣ IsChainComplexCategory( arg ) | ( filter ) |
Returns: true or false
Gap-categories of the chain complexes category.
‣ IsBoundedChainComplexCategory( arg ) | ( filter ) |
Returns: true or false
Gap-categories of the chain complexes category.
‣ IsCochainComplexCategory( arg ) | ( filter ) |
Returns: true or false
Gap-category of the cochain complexes category.
‣ IsBoundedCochainComplexCategory( arg ) | ( filter ) |
Returns: true or false
Gap-category of the cochain complexes category.
‣ ChainComplexCategory( A ) | ( attribute ) |
Returns: a CAP category
Creates the chain complex category \(\mathrm{Ch}_\bullet(A)\) an additive category \(A\). If you want to contruct the category without finalizing it so that you can add your own methods, you can run the command \(\texttt{ChainComplexCategory(A : FinalizeCategory := false )}\).
‣ CochainComplexCategory( A ) | ( attribute ) |
Returns: a CAP category
Creates the cochain complex category \(\mathrm{Ch}^\bullet(A)\) an additive category \(A\). If you want to contruct the category without finalizing it so that you can add your own methods, you can run the command \(\texttt{CochainComplexCategory(A : FinalizeCategory := false )}\).
‣ UnderlyingCategory( B ) | ( attribute ) |
Returns: a CAP category
The input is a chain or cochain complex category \(B=C(A)\) constructed by one of the previous commands. The outout is \(A\)
‣ FullSubcategoryGeneratedByComplexesConcentratedInDegree( B, n ) | ( operation ) |
Returns: a CAP category
The input is a chain or cochain complex category \(B=C(A)\) and an integer \(n\). The outout is the additive full subcategory generated by complexes concentrated in degree \(n\).
‣ AddIsNullHomotopic( Com(A), F ) | ( operation ) |
Returns: true or false
The input is chain (or cochain category) \(Com(A)\) of some additive category \(A\) and a function \(F\). This operation adds the given function \(F\) to the category \(Com(A)\) for the basic operation IsNullHomotopic. So, \(F\) should be a function whose input is a chain or cochain morphism \(\phi\in Com(A)\) and output is true if \(\phi\) is null-homotopic and false otherwise.
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