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2 Functors and natural transformations
 2.1 Functors
 2.2 Natural transformations

2 Functors and natural transformations

2.1 Functors

2.1-1 InclusionFunctorIntoComplexesCategoryByCochains
‣ InclusionFunctorIntoComplexesCategoryByCochains( A )( attribute )

Returns: a CAP functor

Returns the natural inclusion into the complexes category by cochains \(A \to \mathcal{C}^b(A)\).

2.1-2 InclusionFunctorIntoComplexesCategoryByChains
‣ InclusionFunctorIntoComplexesCategoryByChains( A )( attribute )

Returns: a CAP functor

Returns the natural inclusion into the complexes category by chains \(A \to \mathcal{C}^b(A)\).

2.1-3 ExtendFunctorToComplexesCategoriesByCochains
‣ ExtendFunctorToComplexesCategoriesByCochains( F )( attribute )

Returns: a CAP functor

Returns the natural extension of the functor \(F: A \to B\) to the complexes categories by cochains \(\mathcal{C}^b(A) \to \mathcal{C}^b(B)\).

2.1-4 ExtendFunctorToComplexesCategoriesByChains
‣ ExtendFunctorToComplexesCategoriesByChains( F )( attribute )

Returns: a CAP functor

Returns the natural extension of the functor \(F: A \to B\) to the complexes categories by chains \(\mathcal{C}^b(A) \to \mathcal{C}^b(B)\).

2.2 Natural transformations

2.2-1 ExtendNaturalTransformationToComplexesCategoriesByChains
‣ ExtendNaturalTransformationToComplexesCategoriesByChains( eta )( attribute )

Returns: a natural transformation

The input is a natural transformation \(\eta:F\to G\). The output is its extension to the complexes categories by chains.

2.2-2 ExtendNaturalTransformationToComplexesCategoriesByCochains
‣ ExtendNaturalTransformationToComplexesCategoriesByCochains( eta )( attribute )

Returns: a natural transformation

The input is a natural transformation \(\eta:F\to G\). The output is its extension to the complexes categories by cochains.

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