Adjoint Functors

1. Introduction. In homology theory an important role is played by pairs of functors consisting of (i) a functor Horn in two variables, contravariant in the first variable and co-variant in the second (for instance the functor which assigns to every two abelian groups A and B the group Horn (A, B) of homomorphisms/: A—>B). (ii) a functor ® (tensor product) in two variables, covariant in both (for instance the functor which assigns to every two abelian groups A and B their tensor product A®B). These functors are not independent; there exists a natural equivalence