From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7621 Path: news.gmane.org!not-for-mail From: Marco Grandis Newsgroups: gmane.science.mathematics.categories Subject: An old paper on 'cohesive categories' Date: Mon, 11 Mar 2013 18:00:20 +0100 Message-ID: Reply-To: Marco Grandis NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Apple Message framework v753.1) Content-Type: text/plain; charset=WINDOWS-1252; delsp=yes; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1363087678 7064 80.91.229.3 (12 Mar 2013 11:27:58 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 12 Mar 2013 11:27:58 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Tue Mar 12 12:28:23 2013 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1UFNNS-0004wh-7p for gsmc-categories@m.gmane.org; Tue, 12 Mar 2013 12:28:18 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:53894) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1UFNKg-0000h2-2E; Tue, 12 Mar 2013 08:25:26 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1UFNKe-0002dy-H9 for categories-list@mlist.mta.ca; Tue, 12 Mar 2013 08:25:24 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7621 Archived-At: This is to announce a downloadable, slightly revised version of a =20 1988 preprint: Marco Grandis, Cohesive categories and manifolds, Dip. Mat. =20 Univ. Genova, Preprint 76 (1988), published in 1990: =96, Cohesive categories and manifolds, Ann. Mat. Pura Appl. 157 =20= (1990), 199-244. The revised version of the preprint can be found at: http://www.dima.unige.it/~grandis/Chm.Pr1988(Rev.2013).pdf In the present version the text has been slightly modified, to make =20 it less concise and clearer. Moreover, in the proof of the "cohesive =20 completion theorem" (Section 9.2) a correction has been inserted, =20 that was published in: =96, Cohesive categories and manifolds - Errata Corrige, Ann. =20 Mat. Pura Appl. 179 (2001), 471-472. With best regards Marco Grandis ________________________ The purpose of this article is to treat structures, like = manifolds, =20 fibre bundles and foliations, that can be obtained by glueing =20 together 'elementary spaces' of a given kind. These structures are =20 here defined by a sort of glueing atlas, and - formally - as =20 symmetric enriched categories over suitable 2-categories. Their =20 morphisms are defined as 'compatible profunctors'. The basis of the enrichment, called 'cohesive' and 'e-cohesive =20= categories', are equipped with an order and a compatibility relation; =20= they extend inverse categories and the categories of partial =20 mappings. Two completion theorems, with respect to compatible joins =20 and the glueing of 'manifolds', play a crucial role. This matter was presented at the meeting 'Categorical Topology', = =20 Prague 1988 (see [G4]) and is developed in the present work. =20 Applications to partially defined operators between Banach spaces =20 were given in [G5], also published in 1990. The links of this setting with Ehresmann's pseudogroups [E1, E2] = and =20 Lawvere's view of mathematical structures as enriched categories [La] =20= are examined in the Introduction. Dominical categories and p-=20 categories, that are also related with partial mappings and were =20 previously introduced in the 1980's by Heller, Di Paola and Rosolini =20 [He, Di, DH, Ro], have a natural e-cohesive structure (see Section =20 3.8). Later, e-cohesive categories have also been used under the name =20= of 'restriction categories' and equivalent axioms.= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]