On Mon, May 10, 2010 at 2:28 PM, Jeff Egger <jeffegger@yahoo.ca> wrote:
the fact that "autonomous category" is a special case (and, from one point of view, a rather uninteresting special case) of "star-autonomous category", whereas it sounds like "star-autonomous category" should mean an "autonomous category" with some extra structure.
I agree, it does sound like that, but there is at least a long tradition of such names in mathematics (not that that makes them a good thing). (http://ncatlab.org/nlab/show/red+herring+principle) One reason I like "autonomous" to mean a symmetric monoidal category in which all objects have duals is that the only alternative names I have heard for such a thing convey misleading intuition to me. They are sometimes called "compact closed" or (I think) "rigid" monoidal categories, but "compact" and "rigid" are words with definite and inapplicable intuitive meanings for me. Compact means small, finite, bounded, inaccessible by directed joins, etc. and "rigid" means "having few automorphisms," and I don't see that there is anything very compact or rigid about such categories. The only relationship I can think of is that a compact subset of a Hausdorff space is closed, and a symmetric monoidal category with duals for objects is also automatically closed, but of course these two meanings of "closed" are totally different. Perhaps someone can enlighten me? Mike [For admin and other information see: http://www.mta.ca/~cat-dist/ ]