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.
The Ext functors are the right derived functors of the Hom functor. They can be computed by applying to a projective resolution of and taking cohomology.
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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.