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/ ]