 Like many of the concepts in category theory, it was suggested by the needs of homological algebra, which was at the time devoted to computations.Those faced with giving tidy, systematic presentations of the subject would have noticed relations such as

in the category of abelian groups, where "F" was the functor formula_82 (i.e.take the tensor product with "A"), and "G" was the functor hom("A",–) (this is now known as the tensor-hom adjunction).