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contravariant functor

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Show that a contravariant functor takes morphisms that admit left inverses to morphisms that admit right inverses and vice versa.

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Definition. Let C and D be categories. A contravariant functor F : C -> D is a mapping that
(1) associates to each object X element of C an object F(X) element of D
(2) associates to each morphism f: X -> Y in C a morphism F(f) : F(Y) -> F(X) in D such that F(id_x) = id_F(X) and F(please see the attached file).

Show that a contravariant functor takes ...

Solution Summary

This solution characterizes a contravariant functor.