Dear Fred, (my comment is about "more" - not about the terminological question) The group Aut(R) of ring automorphisms of R is well known to be trivial. Proof: (a) Every automorphism takes squares to squares. (b) A real number is a square if and only if it is non-negative. (c) As follows from (a) and (b), every ring automorphism of R preserves order. (d) Aut(Q) is trivial (e) As follows from (c) and (d), Aut(R) is trivial. However, you are right that Q >---> R is not an epimorphism of course. Just use the morphisms into the field C of complex numbers in the same way as you used automorphisms of R. Similarly, using the fact that every algebraic extension of fields of characteristic 0 is separable, it is easy to show that a field extension of characteristic 0 is an epimorphism in the category of commutative rings if and only if it is an isomorphism. Greetings - George ----- Original Message ----- From: "Fred E.J. Linton" <fejlinton@usa.net> To: "categories" <categories@mta.ca> Sent: Wednesday, November 03, 2010 11:40 PM Subject: categories: Terminological question, and more I've been asked for "... the name given in an arbitrary category to an object A for which every mono B----->A is an isomorphism." I'm stumped. Any ideas? I've also been asked to comment on whether "the inclusion Q >-------> R of the ring of rational numbers into that of real ones is a bimorphism, in the category Rng of rings with units and units preserving ring homomorphisms." Reflexively I think: monic, yes; epic, no, as permuting any two independent transcendentals should extend to a non-identity automorphism of R over Q. Am I missing something here? TIA; and cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]