From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6001 Path: news.gmane.org!not-for-mail From: Jiri Rosicky Newsgroups: gmane.science.mathematics.categories Subject: Re: Can one define a "category of all mathematical objects"? Date: Sun, 25 Jul 2010 09:42:48 +0200 Message-ID: Reply-To: Jiri Rosicky NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1280074780 20304 80.91.229.12 (25 Jul 2010 16:19:40 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 25 Jul 2010 16:19:40 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Sun Jul 25 18:19:38 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Od3vL-0000cu-SV for gsmc-categories@m.gmane.org; Sun, 25 Jul 2010 18:19:36 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:59536) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Od3tn-0008CM-SE; Sun, 25 Jul 2010 13:17:59 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Od3tl-000623-Bc for categories-list@mlist.mta.ca; Sun, 25 Jul 2010 13:17:57 -0300 Content-Disposition: inline Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6001 Archived-At: For concrete categories, this problem is addressed in the book A. Pultr and V. Trnkova, Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories, North-Holland 1980. There is a locally small concrete category K containing all locally small concrete categories as full subcategories (up to iso). Assuming the non-existence of a proper class of measurable cardinals, we can take the category Gra of graphs, or the category Smg of semigroups for K.= =20 Without this set-theoretic axiom, both Gra and Smg contain all accessible= =20 categories (i.e., all Grothendieck toposes) as full subcategories. This can be found in my book (with J. Adamek) Locally Presentable=20 and Accessible Categories, Cambridge Univ. Press 1994 ----- Forwarded message from Mattias Wikstr=F6m ----- > Date: Fri, 23 Jul 2010 09:49:26 +0200 > From: Mattias Wikstr=F6m > To: categories@mta.ca > Subject: categories: Can one define a "category of all mathematical obj= ects"? >=20 > 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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]