From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/642 Path: news.gmane.org!not-for-mail From: David Espinosa Newsgroups: gmane.science.mathematics.categories Subject: decompositions of topoi Date: Wed, 11 Feb 1998 12:19:08 -0800 Message-ID: <199802112019.MAA05022@blackhawk.kestrel.edu> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241017091 26659 80.91.229.2 (29 Apr 2009 14:58:11 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:58:11 +0000 (UTC) Cc: espinosa@kestrel.edu To: categories@mta.ca Original-X-From: espinosa@kestrel.edu Wed Feb 11 16:20:04 1998 Original-Received: from kestrel.kestrel.edu (root@ws103.kestrel.edu [206.159.212.104]) by mailserv.mta.ca (8.8.8/8.8.8) with SMTP id QAA05340 for ; Wed, 11 Feb 1998 16:19:34 -0400 (AST) Original-Received: from blackhawk.kestrel.edu by kestrel.kestrel.edu (4.1/SMI-DDN) id AA23262; Wed, 11 Feb 98 12:19:21 PST Original-Received: by blackhawk.kestrel.edu (SMI-8.6/SMI-SVR4) id MAA05022; Wed, 11 Feb 1998 12:19:08 -0800 Original-Lines: 30 Xref: news.gmane.org gmane.science.mathematics.categories:642 Archived-At: Page 216 of Lambek and Scott describes how to decompose a topos via a cocover, that is, a monomorphism in Top M : T -> prod(i in I) T/P_i where P_i are the prime filters of T. (1) Does anyone know where to find a more extended discussion of this decomposition? (2) Is there a dual decomposition via a cover, that is, an epimorphism E : sum(i in I) T_i -> T ? This construction could already be in Lambek and Scott, but I haven't had the chance to study L&S in detail, so I'm still in over my head. The conjecture (due to Y.V. Srinivas) is that these ideas are useful for structuring a database of theories by breaking theories into their smallest reasonable subtheories. See the paper on Specware by Srinivas and Jullig on Kestrel's website http://www.kestrel.edu for more information. So far, this work has dealt with covers of theories, rather than cocovers, whence my question. David Espinosa Kestrel Institute