From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1029 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: Reading advice Date: Tue, 02 Feb 1999 23:33:02 -0800 Message-ID: <199902030733.XAA30719@coraki.Stanford.EDU> References: <199902021922.OAA24636@sirocco.cc.mcgill.ca> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241017492 29068 80.91.229.2 (29 Apr 2009 15:04:52 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:04:52 +0000 (UTC) To: categories@mta.ca Original-X-From: cat-dist Wed Feb 3 04:41:38 1999 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id DAA20419 for categories-list; Wed, 3 Feb 1999 03:42:47 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f In-reply-to: Your message of "Tue, 02 Feb 1999 14:21:45 EST." <199902021922.OAA24636@sirocco.cc.mcgill.ca> Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 20 Xref: news.gmane.org gmane.science.mathematics.categories:1029 Archived-At: >From: "Prof. J. Lambek" >Subject: categories: Reading advice > >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. In view of this would it be fair to say that coherence is not a notion intrinsic to category theory, but rather arises from the traditional set theoretic presentation (or at least point of view) of category theory? Much the same can surely be said of naturality, whose abstract essence is that of 2-cells but which is standardly presented concretely, where the interchange axiom becomes a not entirely trivial theorem. Vaughan Pratt