From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8245 Path: news.gmane.org!not-for-mail From: =?iso-8859-1?Q?Jean_B=E9nabou?= Newsgroups: gmane.science.mathematics.categories Subject: Re: A brief survey of cartesian functors Date: Mon, 28 Jul 2014 13:58:03 +0200 Message-ID: References: <1B862C69106C4B6A83703605D3E6A693@ACERi3> Reply-To: =?iso-8859-1?Q?Jean_B=E9nabou?= NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Apple Message framework v1283) Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1406554243 18421 80.91.229.3 (28 Jul 2014 13:30:43 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 28 Jul 2014 13:30:43 +0000 (UTC) Cc: "Categories" To: "George Janelidze" Original-X-From: majordomo@mlist.mta.ca Mon Jul 28 15:30:37 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1XBl0a-000380-Px for gsmc-categories@m.gmane.org; Mon, 28 Jul 2014 15:30:32 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:48707) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1XBl0K-0006eZ-7R; Mon, 28 Jul 2014 10:30:16 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1XBl0J-00031j-4e for categories-list@mlist.mta.ca; Mon, 28 Jul 2014 10:30:15 -0300 In-Reply-To: <1B862C69106C4B6A83703605D3E6A693@ACERi3> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8245 Archived-At: Dear George,=20 As i mentioned in my mail, it took me many years to develop foliated = categories AND cartesian functors to their full extent. The very first = approach starts circa 1984 when I had proved important results on = cartesian functors between fibered categories and started wondering = about possible generalizations. Thank you for sending me the paper of Cassidy, Herbert and Kelly which I = do not know. I shall look at it carefully, but I doubt very much that it = will have ANYTHING to do with foliated categories, let alone cartesian = functors which are the essential content of my mail. I shall explain why after I have read the paper you are sending me. Best regards to all, Jean Le 28 juil. 2014 =E0 12:52, George Janelidze a =E9crit : > Dear Jean, >=20 > I remember you talking about foliations more than 20 years ago, but = when exactly is this done? Long before? >=20 > No matter what was done first, I think it would nice to compare this = carefully with the results of >=20 > [C. Cassidy, M. H=E9bert, and G. M. Kelly, Reflective subcategories, = localizations, and factorization systems, Journal of Australian = Mathematical Society (Series A), 1985, 287-329]. >=20 > The seemingly big difference is that the above-mentioned paper is = about reflections, but in fact having the right adjoint is a much weaker = restriction than it seems (in this context). >=20 > Since we don't sent attachments to Categories mailing list, I shall = send you that paper separately. >=20 > With best regards to all, > George >=20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]