From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7920 Path: news.gmane.org!not-for-mail From: Marco Grandis Newsgroups: gmane.science.mathematics.categories Subject: preprint Date: Mon, 18 Nov 2013 11:51:29 +0100 Message-ID: Reply-To: Marco Grandis NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Apple Message framework v753.1) Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1384821861 20642 80.91.229.3 (19 Nov 2013 00:44:21 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 19 Nov 2013 00:44:21 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Tue Nov 19 01:44:27 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 1ViZQY-0005z1-Si for gsmc-categories@m.gmane.org; Tue, 19 Nov 2013 01:44:27 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:40629) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1ViZP9-0004BJ-Rx; Mon, 18 Nov 2013 20:42:59 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1ViZPA-0001Dt-6i for categories-list@mlist.mta.ca; Mon, 18 Nov 2013 20:43:00 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7920 Archived-At: The following preprint is available: ------- E. Carletti - M. Grandis Fundamental groupoids as generalised pushouts of codiscrete groupoids Dip. Mat. Univ. Genova, Preprint 603 (2013). http://www.dima.unige.it/~grandis/GpdClm.pdf Abstract. Every differentiable manifold X has a =91good cover=92, where =20= all open sets and their finite intersections are contractible. Using =20 a generalised van Kampen theorem for open covers we deduce that the =20 fundamental groupoid of X is a =91generalised pushout=92 of codiscrete =20= groupoids and inclusions. This fact motivates the present brief study of generalised pushouts. =20 In particular, we show that every groupoid is up to equivalence a =20 generalised pushout of codiscrete subgroupoids, and that (in any =20 category) finite generalised pushouts amount to ordinary pushouts and =20= coequalisers. ------- Before submitting it, I would like to know if the =91generalised =20 pushouts=92 we are using (or similar colimits) have been considered =20 elsewhere. (They are not simply connected colimits, in the sense of Bob Pare, =20 and indeed they cannot be constructed with pushouts.) With best regards to all colleagues and friends. In particular to =20 Ronnie Brown and Bob Pare, whose results are used in this preprint. Marco= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]