From: Paul Levy <pbl@cs.bham.ac.uk>
To: categories@mta.ca
Subject: zigzag category
Date: Tue, 9 Mar 2010 15:12:04 +0000 [thread overview]
Message-ID: <E1NpK7a-0000ig-70@mailserv.mta.ca> (raw)
For a set A, let Cat(A) be the category whose objects are small
categories with object set A, and whose morphisms are identity-on-
objects functors.
For a small category C, let zigzag(C) be the coproduct of C and C^op
within Cat(ob C).
Explicitly, in zigzag(C), a non-identity morphism z : a ---> b is a
nonempty sequence of non-identity C-morphisms that alternately go
forwards or backwards. Depending on the direction of the first and
last C-morphism, z can take one of four different forms.
Surely this appears in the literature? Google gave me a zillion
categorical papers that mention zigzags, but I didn't find this
construction, although several were close (e.g. the special case where
C is the free category on a graph).
Paul
--
Paul Blain Levy
School of Computer Science, University of Birmingham
+44 (0)121 414 4792
http://www.cs.bham.ac.uk/~pbl
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next reply other threads:[~2010-03-09 15:12 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-03-09 15:12 Paul Levy [this message]
2010-03-10 17:16 ` Chris Heunen
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=E1NpK7a-0000ig-70@mailserv.mta.ca \
--to=pbl@cs.bham.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).