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in C with an object in D,
* associates each morphism in C with a morphism in D such that the following two conditions hold:
** for every object in C,
** for all morphisms and in C.

Variance of functor (composite)
* The composite of two functors of the same variance:
**
**
* The composite of two functors of opposite variance:
**
**

Note that contravariant functors reverse the direction of composition.

Ordinary functors are also called covariant functors in

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