From: "Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>
To: John Stell <J.G.Stell@leeds.ac.uk>
Cc: "'categories@mta.ca'" <categories@mta.ca>
Subject: Re: categories with several compositions?
Date: Wed, 2 Feb 2011 15:17:42 +0000 (GMT) [thread overview]
Message-ID: <E1Pkn7Q-0000VY-24@mlist.mta.ca> (raw)
In-Reply-To: <E1PkdTT-0005tx-AB@mlist.mta.ca>
On Wed, 2 Feb 2011, John Stell wrote:
>
> Can anyone tell me whether these structures have been studied anywhere?
>
> A kind of generalized monoid with two or more compositions *1, *2, etc
> with a single identity that works for both and where
> (x *i y) *j z = x *i (y *j z) for all i,j
>
Substituting the common identity for y in this equation yields
x *j z = x *i z, so the compositions all coincide. Similarly
in the multiple-object case.
Peter Johnstone
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2011-02-02 15:17 UTC|newest]
Thread overview: 8+ messages / expand[flat|nested] mbox.gz Atom feed top
2011-02-02 9:58 John Stell
2011-02-02 15:17 ` Prof. Peter Johnstone [this message]
[not found] ` <alpine.LRH.2.00.1102021515540.6678@siskin.dpmms.cam.ac.uk>
2011-02-02 16:11 ` John Stell
2011-02-03 11:36 ` N.Bowler
2011-02-04 18:47 ` Francisco Lobo
2011-02-03 11:56 ` N.Bowler
2011-02-03 12:10 ` N.Bowler
2011-02-03 0:05 categories " Fred E.J. Linton
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=E1Pkn7Q-0000VY-24@mlist.mta.ca \
--to=p.t.johnstone@dpmms.cam.ac.uk \
--cc=J.G.Stell@leeds.ac.uk \
--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).