7 Oct
2002
7 Oct
'02
11:10 a.m.
No. I didn't say that E^T = U^{-1}(E). If, for example, M consists of all monics, then so will M^T (which is defined to be U^{-1}M) and then E^T consists of all extremal epics. For example, in Cat, the image of a functor is not a subcategory, but it certainly generates a subcategory. Under reasonable conditions (arbitrary intersections of M-subobjects) every class M has a complementary class of epics. Michael Barr On Sun, 6 Oct 2002, Bill Rowan wrote:
Hi,
I haven't really looked at your conclusions in detail, but I want to point out that as far as I know, in order for the factorization system E^T/M^T to exist, T (the functor of the triple T) has to send arrows in E into E.
Bill Rowan