From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6352 Path: news.gmane.org!not-for-mail From: Eduardo Ochs Newsgroups: gmane.science.mathematics.categories Subject: Internal Diagrams in Category Theory Date: Tue, 2 Nov 2010 22:41:58 -0200 Message-ID: Reply-To: Eduardo Ochs NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1288799936 442 80.91.229.12 (3 Nov 2010 15:58:56 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 3 Nov 2010 15:58:56 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Wed Nov 03 16:58:52 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PDfjf-00031d-1K for gsmc-categories@m.gmane.org; Wed, 03 Nov 2010 16:58:51 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:50616) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PDfig-0002yA-Fn; Wed, 03 Nov 2010 12:57:50 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PDfid-0005Nf-RN for categories-list@mlist.mta.ca; Wed, 03 Nov 2010 12:57:47 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6352 Archived-At: Hello, I think that following preprint might be of interest to some people on the list: Title: Internal Diagrams in Category Theory Abstract: We can regard operations that discard information, like specializing to a particular case or dropping the intermediate steps of a proof, as _projections_, and operations that reconstruct information as _liftings_. By working with several projections in parallel we can make sense of statements like "$\Set$ is the archetypal Cartesian Closed Category", which means that proofs about CCCs can be done in the "archetypal language" and then lifted to proofs in the general setting. The method works even when our archetypal language is diagrammatical, has potential ambiguities, is not completely formalized, and does not have semantics for all terms. We illustrate the method with an example from hyperdoctrines and another from synthetic differential geometry. It is at: http://angg.twu.net/LATEX/2010diags.pdf Best wishes to all, Eduardo Ochs eduardoochs@gmail.com http://angg.twu.net/ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]