An adjunction has a functorial mono-epi factorization, so natural to be likely well known. I would like to have a *reference* for this. Let F -| G, where F: X --> A and G: A --> X. Then our adjunction has an obvious factorisation through the isomorphic comma categories: W = (F | A) = (X | G) using the full coreflective embedding of X in W, and the full reflective embedding of A in W. W might be called the 'graph' of the adjunction; or has it been called differently? R. Pare and myself, we have used a similar result for double categories, for a colax double functor left adjoint to a lax one: Thm. 3.7 in 'Adjoints for double categories', to appear in 'Cahiers'. But I need now the result for ordinary categories, for applications to directed homotopy. Best regards Marco Grandis