The observations by Martin Hoffman are interesting. In the interests of clarity, I do object to his calling the category of pullback squares the category of Mal'cev relations. One is an existential structure, while the other builds the thing that exists into the structure. It makes it into an entirely different category. Not less interesting, but different. It is (somewhat) like the difference between the categories of complete lattices and complete semilattices. One interesting (and trivial) observation is that if Mal'cev relations are effective, then a quotient of a subobject of a quotient. This is (like everything I've said, but forget to mention) in the presence of sufficient limits and colimits. Now if one could show that the amalgamation property held, one would have that a pushout of a mono is mono in that case. Michael ==========================================================================