From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/10328 Path: news.gmane.io!.POSTED.blaine.gmane.org!not-for-mail From: Venkata Rayudu Posina Newsgroups: gmane.science.mathematics.categories Subject: Re: Roos theorem Date: Wed, 2 Dec 2020 17:24:13 +0530 Message-ID: Reply-To: Venkata Rayudu Posina Mime-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Injection-Info: ciao.gmane.io; posting-host="blaine.gmane.org:116.202.254.214"; logging-data="2709"; mail-complaints-to="usenet@ciao.gmane.io" To: categories Original-X-From: majordomo@rr.mta.ca Thu Dec 03 03:34:23 2020 Return-path: Envelope-to: gsmc-categories@m.gmane-mx.org Original-Received: from smtp2.mta.ca ([198.164.44.74]) by ciao.gmane.io with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.92) (envelope-from ) id 1kkeRr-0000by-IO for gsmc-categories@m.gmane-mx.org; Thu, 03 Dec 2020 03:34:23 +0100 Original-Received: from rr.mta.ca ([198.164.44.159]:44314) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1kkeMk-0001po-Sq; Wed, 02 Dec 2020 22:29:06 -0400 Original-Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1kkePw-0000Ij-Dc for categories-list@rr.mta.ca; Wed, 02 Dec 2020 22:32:24 -0400 Precedence: bulk Xref: news.gmane.io gmane.science.mathematics.categories:10328 Archived-At: If I may, I'd like to add to my earlier question regarding the conditions under which C = B^A the following: If A and B are adequate and discrete, respectively, subcategories of C, then objects of C can be represented as contravariant functors A --> B. Please correct me if I'm mistaken. Also, is this related to the theorem of Roos in SGA4? thank you, posina On Wed, Dec 2, 2020 at 3:48 PM Venkata Rayudu Posina < posinavrayudu@gmail.com> wrote: > > Dear All, > > I hope and pray you and your family are all safe and well. > > I was wondering under what conditions a category C can be written as > an exponential B^A (a category of contravariant functors interpreting > a theory A into a background B). Reyes, Reyes, and Zolfaghari note > (on p. 81 of their book: Generic Figures and their Glueings) that the > answer to the above question is a theorem of Roos in SGA4, p. 415. > > Would you be kind enough to direct me to an English version of Roos theorem. > > thank you, > posina [For admin and other information see: http://www.mta.ca/~cat-dist/ ]