David Leduc wrote:
I'm not sure what [_._] is supposed to mean - an internal hom functor?
This was supposed to be the "cartesian closed structure" of StrictOmegaCat, but since some say it is not a structure I'm not sure how to call it...
Just call it the internal hom. The point is, you can just look at a category and say, yes or no, whether it's cartesian closed. So cartesian closedness is a "property" of a category - not a "structure" that you might equip a category with in more than one way. Nonetheless, you can consider properties as a special case of structures - namely, those structures for which you have at most one one choice. And if you do this you're free to speak of a cartesian closed "structure". Similarly, you can consider structures as a special case of "stuff". If you don't know the yoga of "properties, structure and stuff", you might enjoy this paper where Mike Shulman and I explain it: http://arxiv.org/PS_cache/math/pdf/0608/0608420v2.pdf#page=15 Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]