adjoint functor

(The special case in Cat of the general notion of adjunction.) The concept of adjoint functors [Kan (1958)] is a key concept in category theory — if not the key concept — and it is in large part through the manifold identification of examples of adjoint functors appearing ubiquitously in the practice of mathematics that category theoretic tools are brought to use in general mathematics. Abstractly, the notion of adjoint functors embodies the concept of representable functors and has as special..