From: categories <cat-dist@mta.ca>
To: categories <categories@mta.ca>
Subject: Re: a characterisation of factorisation systems
Date: Tue, 18 Mar 1997 10:29:00 -0400 (AST) [thread overview]
Message-ID: <Pine.OSF.3.90.970318102849.18729G-100000@mailserv.mta.ca> (raw)
Date: 18 Mar 97 12:42:34 +0200
From: Hans Porst <porst@mathematik.uni-bremen.de>
>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
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1997-03-18 14:29 categories [this message]
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1997-03-17 18:49 categories
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