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### 7 Natural transformations

#### 7.1 Natural isomorphisms from identity functor

##### 7.1-1 NaturalIsomorphismFromIdentityToStandardPresentationOfFpLeftModule
 ‣ NaturalIsomorphismFromIdentityToStandardPresentationOfFpLeftModule( A ) ( attribute )

Returns: a natural transformation \mathrm{Id} \rightarrow \mathrm{StandardPresentationOfFpLeftModule}

The argument is an additve closure category A of a ring. The output is the natural isomorphism from the identity functor to the left standard module functor.

##### 7.1-2 NaturalIsomorphismFromIdentityToStandardPresentationOfFpRightModule
 ‣ NaturalIsomorphismFromIdentityToStandardPresentationOfFpRightModule( A ) ( attribute )

Returns: a natural transformation \mathrm{Id} \rightarrow \mathrm{StandardPresentationOfFpRightModule}

The argument is an additve closure category A of a ring. The output is the natural isomorphism from the identity functor to the right standard module functor.

##### 7.1-3 NaturalIsomorphismFromIdentityToGetRidOfZeroGeneratorsOfFpLeftModule
 ‣ NaturalIsomorphismFromIdentityToGetRidOfZeroGeneratorsOfFpLeftModule( A ) ( attribute )

Returns: a natural transformation \mathrm{Id} \rightarrow \mathrm{GetRidOfZeroGeneratorsOfFpLeftModule}

The argument is an additve closure category A of a ring. The output is the natural isomorphism from the identity functor to the functor that gets rid of zero generators of left modules.

##### 7.1-4 NaturalIsomorphismFromIdentityToGetRidOfZeroGeneratorsOfFpRightModule
 ‣ NaturalIsomorphismFromIdentityToGetRidOfZeroGeneratorsOfFpRightModule( A ) ( attribute )

Returns: a natural transformation \mathrm{Id} \rightarrow \mathrm{GetRidOfZeroGeneratorsOfFpRightModule}

The argument is an additve closure category A of a ring. The output is the natural isomorphism from the identity functor to the functor that gets rid of zero generators of right modules.

##### 7.1-5 NaturalIsomorphismFromIdentityToLessGeneratorsOfFpLeftModule
 ‣ NaturalIsomorphismFromIdentityToLessGeneratorsOfFpLeftModule( A ) ( attribute )

Returns: a natural transformation \mathrm{Id} \rightarrow \mathrm{LessGeneratorsOfFpLeftModule}

The argument is an additve closure category A of a ring. The output is the natural morphism from the identity functor to the left less generators functor.

##### 7.1-6 NaturalIsomorphismFromIdentityToLessGeneratorsOfFpRightModule
 ‣ NaturalIsomorphismFromIdentityToLessGeneratorsOfFpRightModule( A ) ( attribute )

Returns: a natural transformation \mathrm{Id} \rightarrow \mathrm{LessGeneratorsOfFpRightModule}

The argument is an additve closure category A of a ring. The output is the natural morphism from the identity functor to the right less generator functor.

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