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contravariant functors from C to Set are often an important object of study. If A is an object of C, then the functor from C to Set that sends X to Hom_C(X,A) (the set of morphisms in C from X to A) is an example of such a functor. If C is a small category (i.e. the collection of its objects forms a set), then the contravariant functors from C to Set, together with natural transformations as morphisms, form a new category,

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