In this paper we determine a SUMMARY pair of adjoint functors for the categories (T । A) and and (T' । A') where T and T' are functors from to Q and A and A' are objects of A precise dcfinition of a Comma Category (T | A) where T is a functor from a category “g to another category Q and A is an obiect of g, in the sense of Maclane [2 ], can be stated as: The objects of (T | A) are pairs (B, b) with B h: (B,b) 1^1 andb:TB A and the morphisms (B', b') are those morphisms h: B -> B' in^ for ■which b'o Th = b. In the present note we determine a pair of adjoint functors for the categories (T | A) and (T' | A') where, again. T' is a functor from “S to Q and A' is an object of g. Lemma 1: If a: T'-> T' is a natural transformation and u: A A' is a morphism, then for (B, b) in (T | A) the rule (B, b) defines a functor K: (T A) Proof: If we define R on (T' I A') morphisms as: for any f: (B, b) (B, ub a B) (B', b') e R (f) = f such that ub'aB'oT' f = ub aB; that is, the following diagram commutes