From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/10240 Path: news.gmane.io!.POSTED.ciao.gmane.io!not-for-mail From: David Roberts Newsgroups: gmane.science.mathematics.categories Subject: Locally internal stacks as categories of families? Date: Mon, 15 Jun 2020 15:13:37 +0930 Message-ID: Reply-To: David Roberts Mime-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Injection-Info: ciao.gmane.io; posting-host="ciao.gmane.io:159.69.161.202"; logging-data="101149"; mail-complaints-to="usenet@ciao.gmane.io" To: "categories@mta.ca list" Original-X-From: majordomo@rr.mta.ca Wed Jun 17 02:13:18 2020 Return-path: Envelope-to: gsmc-categories@m.gmane-mx.org Original-Received: from smtp2.mta.ca ([198.164.44.55]) by ciao.gmane.io with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.92) (envelope-from ) id 1jlLhe-000QDH-8Q for gsmc-categories@m.gmane-mx.org; Wed, 17 Jun 2020 02:13:18 +0200 Original-Received: from rr.mta.ca ([198.164.44.159]:56854) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1jlLh8-0000uX-PQ; Tue, 16 Jun 2020 21:12:46 -0300 Original-Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1jlLh4-0001ZE-Mq for categories-list@rr.mta.ca; Tue, 16 Jun 2020 21:12:42 -0300 Precedence: bulk Xref: news.gmane.io gmane.science.mathematics.categories:10240 Archived-At: Dear all I=E2=80=99ve had reason to think about locally internal categories/locally small fibrations over a base topos lately, and I was asked to what extent one can view these as categories of families of objects of a =E2=80=9Clocally small category=E2=80=9D in a structural axiomatic set theo= ry. To me it seems like one should take the fibration to be a stack, since given compatible families of objects on some cover, then one should definitely be able to glue them. Maybe I=E2=80=99m looking in the wrong places, but I don=E2=80=99t see any statements to this effect in the variou= s papers on locally internal categories (in all their various guises and names), by Penon, B=C3=A9nabou, Par=C3=A9=E2=80=93Schumacher the Baby Eleph= ant, and The Elephant (to name a few). I didn=E2=80=99t read them thoroughly, but I also didn=E2=80=99t see it in Mike Shulman=E2=80=99s Sets for category theory or= Enriched indexed categories. Does anyone else concur, or know of a result in the literature close to thi= s? Regards, David David Roberts Webpage: https://ncatlab.org/nlab/show/David+Roberts Blog: https://thehighergeometer.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]