From: "Dr. P.T. Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>
To: categories@mta.ca
Subject: Re: Reference?
Date: Fri, 30 Oct 1998 09:26:24 +0000 (GMT) [thread overview]
Message-ID: <E0zZAp7-0001aE-00@owl.dpmms.cam.ac.uk> (raw)
>
> Can someone give me a reference for the fact that if the hom functor on a
> category factors through commutative monoids then finite products are sums
> and vice versa. Also conversely.
>
> Michael
Mac Lane (Categories for the Working Mathematician) does one direction
in Theorem 2 on page 190. (He assumes enrichment over abelian groups
rather than commutative monoids, but a glance at the proof shows that
the additive inverses are not used.) The converse is stated as Exercise
4 on page 194.
Peter Johnstone
next reply other threads:[~1998-10-30 9:26 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
1998-10-30 9:26 Dr. P.T. Johnstone [this message]
-- strict thread matches above, loose matches on Subject: below --
1998-10-30 16:02 Reference? F W Lawvere
1998-10-29 19:00 Reference? Michael Barr
1998-11-03 11:19 ` Reference? boerger
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=E0zZAp7-0001aE-00@owl.dpmms.cam.ac.uk \
--to=p.t.johnstone@dpmms.cam.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).