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From: Steve Vickers <s.j.vickers@cs.bham.ac.uk>
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Subject: Re: comparing cotriples via an adjoint pair
Date: Mon, 24 May 2004 10:04:38 +0100
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This paper may also be relevant (again in the dual situation, with monads):

   Jean-Pierre Meyer "Induced functors on categories of algebras",
Mathematische Zeitschrift 142 (1975) 1-14.

This relaxes the condition that it should be a natural isomorphism
between RT and SR. Instead it has a monad functor from (D,T) to (C,S)
and a left adjoint monad opfunctor. It constructs an adjoint pair of
functors between the algebra categories. However, it does assume that
one of the algebra categories has coequalizers.

For monad functors and opfunctors see

   Ross Street "The formal theory of monads", Journal of Pure and
Applied Algebra 2 (1972) 149-168.

Steve Vickers.

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