From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/904 Path: news.gmane.org!not-for-mail From: "Dr. P.T. Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: Reference? Date: Fri, 30 Oct 1998 09:26:24 +0000 (GMT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241017312 28218 80.91.229.2 (29 Apr 2009 15:01:52 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:01:52 +0000 (UTC) To: categories@mta.ca Original-X-From: cat-dist Fri Oct 30 13:11:19 1998 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id LAA31103 for categories-list; Fri, 30 Oct 1998 11:24:24 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 16 Xref: news.gmane.org gmane.science.mathematics.categories:904 Archived-At: > > 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