do the torsors of a group g form a closed category (in the sense of eilenberg and kelly, or something...)?? they don't form a monoidal category unless g is abelian ... ????...

if so then what about categories enriched over it?? for example itself... ???...

what about the free cartesian closed category on an object x equipped with an isomorphism (??perhaps with some nice "coherence" property?) to x^x? what about some sort of combinatorial-game interpretation of this??

hmm, there's definitely some confusion here... between internal and external hom, for one thing... the external hom from one torsor to another is naturally a torsor, but ... ???? ??or something??

i guess that there's lots of examples of a category c equipped with a factorization of its hom bifunctor through itself that don't give a closed category; for example lots of examples where c is discrete... is that correct?

maybe this is "worse" than that, though... i'm still somewhat confused here...