On Wed, 3 Nov 2010, Fred E.J. Linton wrote:
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?
The obvious thing is to borrow a word from ordered set theory and call it a minimal object. (All morphisms in a poset are monic.) The term "strict initial object" is well-established for an initial object 0 such that *every* morphism A --> 0 is an isomorphism. I've sometimes been tempted to use "strict object" for this property without the assumption of initiality; but the trouble is that you then have to say "costrict object" for the dual property, which doesn't seem right. Peter Johnstone [For admin and other information see: http://www.mta.ca/~cat-dist/ ]