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/ ]