From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1028 Path: news.gmane.org!not-for-mail From: "Prof. J. Lambek" Newsgroups: gmane.science.mathematics.categories Subject: Reading advice Date: Tue, 2 Feb 1999 14:21:45 EST Message-ID: <199902021922.OAA24636@sirocco.cc.mcgill.ca> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241017491 29060 80.91.229.2 (29 Apr 2009 15:04:51 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:04:51 +0000 (UTC) To: categories@mta.ca Original-X-From: cat-dist Tue Feb 2 20:12:00 1999 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id TAA29354 for categories-list; Tue, 2 Feb 1999 19:12:09 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 15 Xref: news.gmane.org gmane.science.mathematics.categories:1028 Archived-At: Concerning the question by Lindquist: The tensor product automatically satisfies all functoriality, associativity and coherence conditions, if it is introduced by a universal property as by Bourbaki. This is shown for monoidal categories (bicategories with one object) e.g. in my paper ``Multicategories revisited'', Contemporary Mathematics 92(1989). The same argument works for arbitrary bicategories provided, in defining a multicategory, one replaces the free monoid generated by a set by the free category generated by a graph. Jim Lambek