Re: comparing cotriples via an adjoint pair

["Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>]

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unpublished (and largely unwritten) thesis of Bill Butler.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