‣ 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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