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From: "Dr. P.T. Johnstone"
Newsgroups: gmane.science.mathematics.categories
Subject: Re: Reference?
Date: Fri, 30 Oct 1998 09:26:24 +0000 (GMT)
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>
> 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