From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4559 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Re: Categories and functors, query Date: Wed, 10 Sep 2008 17:20:45 -0700 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1241020026 13853 80.91.229.2 (29 Apr 2009 15:47:06 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:06 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Sep 11 14:20:13 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 11 Sep 2008 14:20:13 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KdpjZ-00017R-Sp for categories-list@mta.ca; Thu, 11 Sep 2008 14:13:33 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 29 Original-Lines: 24 Xref: news.gmane.org gmane.science.mathematics.categories:4559 Archived-At: Dana Scott wrote in part: >But, as >everyone knows, it is not the definition of a category that >is the key part, but seeing that functors and natural >transformations are interesting. Indeed, the notion of natural isomorphism (or canonical isomorphism) should be available already to groupoid theorists before 1945. To what extent did they know about functors and natural isomorphisms, and to what extent did Saunders & Mac Lane have to tell them? Or, pace Walter's remarks, did they know about the ~small~ ones but not have the guts to apply them to large classes of strucures? It's been said before that the real insight of category theory --as something more general than groupoids, monoids, and posets-- is the notion of adjoint functors (including limits, etc). I'm inclined to agree, so I'm interested in why and whether groupoid theorists thought of (and applied) that which they ~did~ have. --Toby