From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5530 Path: news.gmane.org!not-for-mail From: John Baez Newsgroups: gmane.science.mathematics.categories Subject: Re: forms Date: Thu, 14 Jan 2010 18:51:00 -0800 Message-ID: Reply-To: John Baez NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: ger.gmane.org 1263598201 25744 80.91.229.12 (15 Jan 2010 23:30:01 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 15 Jan 2010 23:30:01 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Sat Jan 16 00:29:54 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1NVvc1-0001GE-8a for gsmc-categories@m.gmane.org; Sat, 16 Jan 2010 00:29:53 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NVvAD-0002tQ-2T for categories-list@mta.ca; Fri, 15 Jan 2010 19:01:09 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5530 Archived-At: 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/ ]