From: "Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>
To: Michael Barr <barr@math.mcgill.ca>
Cc: Categories list <categories@mta.ca>
Subject: Re: Derived cotriples
Date: Tue, 22 May 2012 17:34:25 +0100 (BST) [thread overview]
Message-ID: <E1SWsul-0006sV-EU@mlist.mta.ca> (raw)
In-Reply-To: <E1SWrfE-0006bv-Tb@mlist.mta.ca>
The dual construction was studied by Sabah Fakir in "Monade idempotente
associee a une monade", C.R. Acad. Sci. Paris 270 (1970), A99-101.
Peter Johnstone
On Mon, 21 May 2012, Michael Barr wrote:
> 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 prev parent reply other threads:[~2012-05-22 16:34 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2012-05-21 21:23 Michael Barr
2012-05-22 16:34 ` Prof. Peter Johnstone [this message]
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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