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### 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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