In category theory, the Hom functor is a fundamental concept used to describe morphisms (arrows) between objects in a category. Specifically, given a category \(\mathcal{C}\), the Hom functor allows us to examine the set of morphisms between two object types. ### Definition 1.
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The Hom functor sends two -modules to the abelian group of -linear maps between them. It is contravariant in its first argument and covariant in its second.