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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




             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

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