From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3884 Path: news.gmane.org!not-for-mail From: Michal Przybylek Newsgroups: gmane.science.mathematics.categories Subject: Re: Teaching Category Theory Date: Thu, 06 Sep 2007 00:36:21 +0200 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7BIT X-Trace: ger.gmane.org 1241019581 10720 80.91.229.2 (29 Apr 2009 15:39:41 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:39:41 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Sep 5 20:25:13 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 05 Sep 2007 20:25:13 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IT4CJ-00046j-Dx for categories-list@mta.ca; Wed, 05 Sep 2007 20:22:11 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 8 Original-Lines: 35 Xref: news.gmane.org gmane.science.mathematics.categories:3884 Archived-At: "Jeff Egger" wrote: > --- Michael Shulman wrote: > My guess would be that it's because for non-category theorists, many > (perhaps most) categories which arise in practice are enriched (over > something more exotic than Set), while few are internal (to something > more exotic than Set). I think it's not that. It's just because the concept of internal category is in some sense subsumed by the concept of fibration. And in practical situations we prefer to work with fibrations rather than internal categories. > Actually, currently my favorite level of generality is something I > call a "monoidal fibration". Roughly, the idea is that you have two > different "base" categories, S and V, such that the object-of-objects > comes from S while the object-of-morphisms comes from V. When S and V > are the same, you get internal categories, and when S=Set, you get > classical enriched categories. What do you mean by "you get internal/enriched categories" ? Do you have a 2-equivalence between the 2-category of all S-internal (resp. enriched) categories (S-internal functors, S-internal natural transformations) and the 2-category of your categories ? I'm asking because I have encountered some difficulties here (i.e. in my framework some diagrams are not willing to commute "on the nose"). Best regards, Michal R. Przybylek