From: Oswald Wyler <owyler@suscom-maine.net>
To: categories@mta.ca
Subject: Re: comparing cotriples via an adjoint pair
Date: Sat, 22 May 2004 11:17:59 -0400 (EDT) [thread overview]
Message-ID: <Pine.LNX.4.44.0405221056550.23060-100000@203-228.suscom-maine.net> (raw)
In-Reply-To: <5.1.0.14.2.20040520232118.0235f070@mailbox.syr.edu>
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
This situation has been encountered since at least 1970 by various
categorists, including myself. A relevant paper is:
D. Pumpl\"un, Eine Bemerkung \"uber Monaden und adjungierte Funktoren,
Math. Annalen 185, 329-337 (1970).
If Gaunce's two commuting diagrams are the usual ones, then his
conjecture is correct. Observe that in this situation, we have not just
a pair but a quadruple of dual categories, replacing C and D by their
duals, or inverting the direction of arrows, or both.
This may just be a "folk theorem", but it should have been published by
someone, somewhere, and I would also like to have an easily accessible
reference, or references.
Oswald Wyler
next prev parent reply other threads:[~2004-05-22 15:17 UTC|newest]
Thread overview: 6+ messages / expand[flat|nested] mbox.gz Atom feed top
2004-05-21 3:28 Gaunce Lewis
2004-05-21 20:30 ` Michael Barr
2004-05-21 20:54 ` Prof. Peter Johnstone
2004-05-22 15:17 ` Oswald Wyler [this message]
2004-05-24 9:04 ` Steve Vickers
2004-05-31 13:52 Claudio Hermida
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