Definition talk:Isomorphism (Abstract Algebra)

Aren't there categories in which a mono-epi is not an iso? For example, monoid categories (but maybe it is provable in case we are dealing with a 'set-category' of sets and certain special functions). --Lord_Farin 18:46, 23 March 2012 (EDT)


 * If there are, I haven't heard of them. My understanding is: a mono is an injective homo, an epi is a surjective homo, a mono-epi is an inj-surj homo i.e. a bijective homo, i.e. an iso.
 * If there are categories out there which do not fit into this system, I haven't heard of them. If you have, please share. --prime mover 18:56, 23 March 2012 (EDT)
 * Well I am only just venturing into category theory with the arrival of two books; when time comes, I will think about this stuff. But one of them explicitly says:
 * 'So it is clear that every iso is a mono-epi. However, the converse is, in general, false. For example, take a monoid category'.
 * But I'm not sure as of yet how to interpret this, so I'll leave it for now. --Lord_Farin 19:32, 23 March 2012 (EDT)


 * Bear in mind that the definitions are different for category theory. The disambiguation pages are in place: there are two versions, one for Abs Alg and one for Cat Thry. And epi and mono look a bit different in cat thry to in abs alg. --prime mover 20:16, 23 March 2012 (EDT)