From: Tobias Heindel <tobias.heindel@uni-due.de>
To: categories@mta.ca
Subject: The converse of universality/pullback-stability
Date: Tue, 08 Dec 2009 11:33:50 +0100 [thread overview]
Message-ID: <E1NIAs0-0006XA-3Y@mailserv.mta.ca> (raw)
I have a short question concerning terminology related to extensive
categories. In the latter, coproducts enjoy the following property.
U ----> Z <---- V
| | |
| | |
v v v
A ---> A+B <--- B
/--------------------------------------------\
| In a double square diagram as illustrated, |
| the top row is a coproduct diagram |
| if and only if both squares are pullbacks. |
\--------------------------------------------/
The "if"-part of this condition is known as universality or
pullback-stability of co-products; it also can be formulated for
arbitrary colimits. What about the "only if" direction? Is there a
name for it in the case of arbitrary colimits?
Tobias Heindel
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
reply other threads:[~2009-12-08 10:33 UTC|newest]
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