Re: forms

[John Baez <john.c.baez@gmail.com>]

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


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