From: Michael Barr <barr@math.mcgill.ca>
To: Categories list <categories@mta.ca>
Subject: Derived cotriples
Date: Mon, 21 May 2012 17:23:29 -0400 (EDT) [thread overview]
Message-ID: <E1SWrfE-0006bv-Tb@mlist.mta.ca> (raw)
Suppose (G,\epsilon,\delta) is a cotriple on a complete category. Let G^2
===> G ---> G' be a coequalizer. Then we can find canonical (perhaps
unique) \epsilon': G' ---> Id and \delta': G' ---> G'^2 such that
(G',\epsilon',\delta') is a new cotriple on the category and such that G
---> G' is a map of cotriples. It seems reasonable to call this the
derived cotriple. This process can be repeated, apparently forever, using
colimits at limit ordinals. If it ever stablizes, the resultant cotriple
will be idempotent and vice versa. Does any know whether this construction
has been studied before?
Michael
--
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next reply other threads:[~2012-05-21 21:23 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2012-05-21 21:23 Michael Barr [this message]
2012-05-22 16:34 ` Prof. Peter Johnstone
2012-05-22 21:37 ` Ross Street
2012-05-22 17:41 ` Eduardo J. Dubuc
2012-05-22 22:35 ` Donovan Van Osdol
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