Al Vilcius wrote:
For example, in vector spaces (k-mod)
there are the usual bijective correspondences:
X tensor Y ---> Z linear in k-mod ____________________________________
X cartesian Y ---> Z bilinear
Andrej Bauer replied:
I always understood the correspondence between the first and the second line as saying "don't talk about bilinear maps on products--talk about linear maps on tensor products instead".
Or, you can reverse your attitude and say "don't talk about linear maps out of tensor products--talk about arrows in the *multicategory* of multilinear maps'. You may not like multicategories - but as Toby said, they're there when you want them, waiting with the kind of patience that only mathematical objects can muster: http://ncatlab.org/nlab/show/multicategory http://en.wikipedia.org/wiki/Multicategory Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]