18 Feb
1992
18 Feb
'92
1:59 p.m.
Here is what I think ought to be the definition in a general category. Say that f:A --> B is a regular epi if whenever g:A --> C is an arrow with the property that [(forall parallel pairs u,v with codmain A) (fu = fv ==> gu = gv)] ==> (exists! h:B --> C) (hf = g). If there is a kernel pair, this is equivalent to the more common definition. Obviously, the dual definition should be used for regular monics. Michael =========================================================================