Date: Fri, 14 Mar 1997 15:26:15 GMT From: Paul-Andre Mellies <paulm@dcs.ed.ac.uk>
Your definition
Let E and M be two classes of morphisms in a category C. (E,M) is a factorisation system of C if and only if the four following properties hold:
1. every morphism f in C can be factored as f=me with m in M and e in E, 2. if e is a morphism in E and m is a morphism in M then e is orthogonal to m, 3. if i is an iso left composable to e in E, then ie is in E, 4. if i is an iso right composable to m in M, then mi is in M.
seems to be precisely the definition used in Adamek, Herrlich, Strecker: Abstract and Concrete Categories. Check their Chapter 14! AHS 14.6 shows in particular that E and M will be closed under composition. --------------------------------------------------------- Hans-E. Porst e-mail: porst@mathematik.uni-bremen.de FB 3: Mathematik Phone: +49 421 2182276 University of Bremen +49 421 2184971 D-28334 Bremen Fax: +49 421 2184856 ---------------------------------------------------------