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From: "Prof. Peter Johnstone"
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Subject: Re: comparing cotriples via an adjoint pair
Date: Fri, 21 May 2004 21:54:06 +0100 (BST)
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On Thu, 20 May 2004, Gaunce Lewis wrote:
> I have encountered a situation in which I have two categories C, D which
> are related by a pair of adjoint functors L from C to D and R from D to
> C. Also, there is a cotriple S on C and a cotriple T on D. Finally, there
> is a natural isomorphism f from RT to SR. It seems that if a couple of
> diagrams relating f to the structure maps of the cotriples commute, then
> there is an induced adjoint pair relating the two coalgebra categories. Is
> this, or something similar to it, in the literature in some easily
> referenced place?
>
> Thanks,
> Gaunce
>
See (for the dual situation) an old paper of mine:
Adjoint lifting theorems for categories of algebras, Bull London Math.
Soc. 7 (1975), 294--297.
I should say (before others say it for me) that this was not the first
place the result appeared: it (and much more) was in the famous
unpublished (and largely unwritten) thesis of Bill Butler. But Gaunce
asked for a published reference.
Peter Johnstone