Subject: categories: Re: Linear categories

From: F W Lawvere <[email-masked]>
Date: Sat, 31 Oct 1998 14:19:05 -0500 (EST)

Dear Mike and everbody
The converse result , as stated by Mac Lane, was what needed to be said in
1950, especially since it began to bring out that category theory has
content. What it's converse to, namely that when maps can be added then
the cartesian product has the mapping property now called coproduct, had
already been folklore for years... or if it hadn't been, how else to
explain the widespread terminological ambiguity concerning "direct sums"?
Perhaps a much older reference needs to be adduced.
Thanks for bringing this up.
Best regards
Bill

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F. William Lawvere			Mathematics Dept. SUNY 
[email-masked]               106 Diefendorf Hall
716-829-2144  ext. 117		        Buffalo, N.Y. 14214, USA

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On Fri, 30 Oct 1998, Michael Barr wrote:

> I have checked Mac Lane's 1950 paper and I cannot find any such result.
> The converse, that a category in which finite sums are equivalent to
> products then the category takes homs in commutative monoids is sort of
> there, but the one I asked is not, or at least I didn't find it.  However,
> CWM is a likely source and I will check that out.  I just need some
> reference in any case.
> 
> Michael
> 
> 
>