  Here are some of the important facts regarding adjoint functors. Firstly, adjoints are unique up to isomorphism; that is any two left adjoints \(F\) and \(F'\) of a functor \(G\) are naturally isomorphic. Secondly, the notion of adjointness is formally equivalent to the notion of a universal morphism (or construction) and to that of representable functor. (See, for instance Mac Lane 1998, chap. IV.) Each and every one of these notions exhibit an aspect of a given situation. Thirdly, a left adjoint preserves all the colimits which exist in its domain, and, dually, a right adjoint preserves all the limits which exist in its domain.