From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4959 Path: news.gmane.org!not-for-mail From: Hasse Riemann Newsgroups: gmane.science.mathematics.categories Subject: RE: Fundamental Theorem of Category Theory? Date: Wed, 10 Jun 2009 02:29:07 +0000 Message-ID: Reply-To: Hasse Riemann NNTP-Posting-Host: lo.gmane.org Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1244682137 8653 80.91.229.12 (11 Jun 2009 01:02:17 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 11 Jun 2009 01:02:17 +0000 (UTC) To: , Category mailing list Original-X-From: categories@mta.ca Thu Jun 11 03:02:15 2009 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 1MEYgI-0000V0-Op for gsmc-categories@m.gmane.org; Thu, 11 Jun 2009 03:02:14 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MEY9a-0000Z8-R8 for categories-list@mta.ca; Wed, 10 Jun 2009 21:28:26 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4959 Archived-At: =20 =20 Dear Ellis =20 I also had this question when i started with category theory but i was satisfied with the Yoneda lemma. Now thanks to your question i know more theorems to answer this. I don't think you can get a better answer than the replied suggestions. =20 However there is also higher category theory. The interesting point would now be to generalize: =20 What are the coresponding theorems for strict/weak n-categories? =20 I plan to at least ask for and suggest a higher dimensional Yoneda lemma. =20 The other adjoints preserving limits theorem is also interesting to generalize. But here as far as i know there is no concept of adjoint for 3-categories and higher up. I am more uncertain as to limits=2C but i have not seen limits in n-categories defined in the graceful style of limits in 1-categories. =20 Best regards Rafael Borowiecki =20 =20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]