Concerning axiomatization of universal algebra using arrows, usually we consider that an identity in universal algebra is given categorically by giving a pair <f,g> of elements of a free algebra F (or, a pair of homomorphisms from a free algebra on one element into F) and then an algebra X satisfies <f,g> iff all homomorphisms F->X coequalize <f,g>. I think this is explained sketchily in MacLane, CWM. This is subsumed by your framework because we only need to form the coequalizer h:F->G of <f,g> and then take {h} as your class A of arrows. Perhaps your framework has greater expressive power than the usual one in universal algebra, in which case it might be worth publishing, but I can offer no strong opinion to that effect, and indeed you will probably have to figure this out yourself. You also need to consider that perhaps someone else has an equivalent or even more general framework which is all worked out, such as sketches or something. Perhaps some other people will have other comments. Bill Rowan +++++++++++++++++++