From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6000 Path: news.gmane.org!not-for-mail From: Dusko Pavlovic Newsgroups: gmane.science.mathematics.categories Subject: Re: Can one define a "category of all mathematical objects"? Date: Sat, 24 Jul 2010 08:48:05 -0700 Message-ID: References: Reply-To: Dusko Pavlovic NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v1081) Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1280015612 13732 80.91.229.12 (24 Jul 2010 23:53:32 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 24 Jul 2010 23:53:32 +0000 (UTC) Cc: categories@mta.ca To: =?iso-8859-1?Q?Mattias_Wikstr=F6m?= Original-X-From: majordomo@mlist.mta.ca Sun Jul 25 01:53:31 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OcoX4-0005pH-Qw for gsmc-categories@m.gmane.org; Sun, 25 Jul 2010 01:53:31 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:51730) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OcoUy-0001uM-Va; Sat, 24 Jul 2010 20:51:20 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OcoUs-0007tO-PB for categories-list@mlist.mta.ca; Sat, 24 Jul 2010 20:51:15 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6000 Archived-At: The Grothendieck Construction provides a somewhat trivial answer: a = category fibered over Cat, where the fiber over each category is that = category. But the object class of this fibered category does not live in = the same universe as the object classes of the objects of Cat. Moreover, = this construction is very redundant: eg each category A is disjoint from = the category A+A, which consists of two copies of A.=20 So the question is really: How can we glue together large families of = categories in a less redundant way? For toposes, the answer seems ti be = Gros Topos. Is this gluing business essentially topological, or are = there other views? just my 2c. -- dusko On Jul 23, 2010, at 12:49 AM, Mattias Wikstr=F6m wrote: > Dear Categorists, >=20 > I would be interested in hearing what you think of an idea that seems > rather wild: Is it possible to define a category with nice properties > such that any locally small category becomes isomorphic to a > subcategory of that category? >=20 > In the absence of such a category, can a category such as the category > of all Grothendieck topoi and geometric morphisms between them serve > as a "category of all mathematical objects" for practical purposes? >=20 > Mattias Wikstrom >=20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]