If "C" is an arbitrary category, the 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, a functor category known as the category of presheaves on "C".