From: F W Lawvere <wlawvere@ACSU.Buffalo.EDU>
To: Categories list <categories@mta.ca>
Subject: Re: Reference?
Date: Fri, 30 Oct 1998 11:02:31 -0500 (EST) [thread overview]
Message-ID: <Pine.GSO.3.96.981030103047.19997A-100000@xena.acsu.buffalo.edu> (raw)
Re: Mike Barr's question concerning two equivalent definitions
of a class of categories
Since the term 'additive' had already been established to refer
to the special case where the homs are abelian groups, I called
these 'linear categories' in my paper
Categories of Space and of Quantity
in The Space of Mathematics, Philosophical, Epistemological
and Historical Explorations, de Gruyter, Berlin (1992) pp 14-30
because 'linear' is a term well known to engineers, statisticians and
others, and because these categories form the natural environment for
applications of Linear Algebra. Of course, the entries in the matrices
are in general maps, not necessarily scalars, although scalars for which
the addition is idempotent are an important special case. (Here by the
scalars of such a category I mean the elements of the rig which is its
center.)
In that paper I referred to what I believe is the first reference
to this theory, namely Saunders Mac Lane's 1950 paper
Duality for Groups, Bull AMS vol 56, pp 485-516, (1950)
expounding work he did in the late 40's.
Bill Lawvere
******************************************************************
F. William Lawvere Mathematics Dept. SUNY
wlawvere@acsu.buffalo.edu 106 Diefendorf Hall
716-829-2144 ext. 117 Buffalo, N.Y. 14214, USA
******************************************************************
On Thu, 29 Oct 1998, Michael Barr wrote:
> 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
>
>
>
next reply other threads:[~1998-10-30 16:02 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
1998-10-30 16:02 F W Lawvere [this message]
-- strict thread matches above, loose matches on Subject: below --
1998-10-30 9:26 Reference? Dr. P.T. Johnstone
1998-10-29 19:00 Reference? Michael Barr
1998-11-03 11:19 ` Reference? boerger
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