Name for a concept

Is there a standard name for a square A ----> B | | | | | | v v C ----> D in which the canonical map A ---> B x_D C is epic? I had always called it a weak pullback, but Peter Freyd claims that that phrase is reserved for the case that it satisfies the existence, but not necessarily the uniqueness of the definition of pullback. In fact, he claims it means that Hom(E,-) converts it to the kind of square I am talking about. What is interesting is that in an abelian category, it satisfies this condition iff it satisfies the dual condition iff the evident sequence A ---> B x C ---> D is exact. Putting a zero at the left end characterizes a genuine pullback and at the other end a pushout. Michael