categories - Category Theory list
 help / color / mirror / Atom feed
From: "Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>
To: Michael Barr <barr@math.mcgill.ca>
Cc: Categories list <categories@mta.ca>
Subject: Re:  Derived cotriples
Date: Tue, 22 May 2012 17:34:25 +0100 (BST)	[thread overview]
Message-ID: <E1SWsul-0006sV-EU@mlist.mta.ca> (raw)
In-Reply-To: <E1SWrfE-0006bv-Tb@mlist.mta.ca>

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
>
>


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]


  reply	other threads:[~2012-05-22 16:34 UTC|newest]

Thread overview: 5+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2012-05-21 21:23 Michael Barr
2012-05-22 16:34 ` Prof. Peter Johnstone [this message]
2012-05-22 21:37   ` Ross Street
2012-05-22 17:41 ` Eduardo J. Dubuc
2012-05-22 22:35 ` Donovan Van Osdol

Reply instructions:

You may reply publicly to this message via plain-text email
using any one of the following methods:

* Save the following mbox file, import it into your mail client,
  and reply-to-all from there: mbox

  Avoid top-posting and favor interleaved quoting:
  https://en.wikipedia.org/wiki/Posting_style#Interleaved_style

* Reply using the --to, --cc, and --in-reply-to
  switches of git-send-email(1):

  git send-email \
    --in-reply-to=E1SWsul-0006sV-EU@mlist.mta.ca \
    --to=p.t.johnstone@dpmms.cam.ac.uk \
    --cc=barr@math.mcgill.ca \
    --cc=categories@mta.ca \
    /path/to/YOUR_REPLY

  https://kernel.org/pub/software/scm/git/docs/git-send-email.html

* If your mail client supports setting the In-Reply-To header
  via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).