From: Michael Shulman <shulman@uchicago.edu>
To: <joyal.andre@uqam.ca>
Subject: Re: Re: bilax_monoidal_functors
Date: Fri, 14 May 2010 23:44:52 -0500 [thread overview]
Message-ID: <E1ODKxA-0006HZ-7J@mailserv.mta.ca> (raw)
On Fri, May 14, 2010 at 8:05 PM, Joyal, Andre <joyal.andre@uqam.ca> wrote:
> I guess that in the category of R-modules over a commutative ring R,
> a module M has a (good) dual iff it is finitely generated projective
> iff the endo-functor functor Hom(M,-) preserves all colimits
> (M is *compact* in a strong sense).
Indeed, but in this case it is the objects of the category which are
"compact," not the category itself. So if this is the argument, then
a more natural term would be "locally compact" (clashing with "locally
small," of course, but agreeing with "locally presentable" categories
in which all objects are presentable).
(I am *not* proposing to *actually* use "locally compact" -- I don't
want to introduce yet another name for something that already has at
least four names, even if none of the existing four are optimal.)
Mike
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next reply other threads:[~2010-05-15 4:44 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-05-15 4:44 Michael Shulman [this message]
-- strict thread matches above, loose matches on Subject: below --
2010-05-08 3:27 RE : bilax monoidal functors John Baez
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