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From: "Prof. Peter Johnstone"
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Subject: Re: Derived cotriples
Date: Tue, 22 May 2012 17:34:25 +0100 (BST)
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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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