From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/248 Path: news.gmane.org!not-for-mail From: Hasse Riemann Newsgroups: gmane.science.mathematics.categories Subject: Smooth and proper functors Date: Wed, 15 Apr 2009 13:45:06 +0000 Message-ID: Reply-To: Hasse Riemann 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: ger.gmane.org 1239820477 15741 80.91.229.12 (15 Apr 2009 18:34:37 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 15 Apr 2009 18:34:37 +0000 (UTC) To: Original-X-From: categories@mta.ca Wed Apr 15 20:35:56 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1Lu9xf-00084e-Qo for gsmc-categories@m.gmane.org; Wed, 15 Apr 2009 20:35:52 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Lu9HX-0006fq-Of for categories-list@mta.ca; Wed, 15 Apr 2009 14:52:19 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:248 Archived-At: =20 Hi category gurus and categorists =20 I have many questions about category theory but i start with one. =20 1> What are smooth functors and proper functors=2C originating in pursuing sta= cks? Both nontechnically and technicaly. =20 I know they are dual to each other and that they are characterized by cohom= ological properties inspired by the proper or smooth base change theorem in algebraic geometry= =2C but what is the relation? (I don't know the statement of the theorems) =20 Finally=2C what are smooth and proper functors good for? Are smooth and proper functors fibrations and cofibrations or Grothendieck = fibrations and Grothendieck op-fibrations in some model categories or derivators? =20 The only thing i could find about smooth and proper functors on internet is= the last entrance in http://golem.ph.utexas.edu/category/2008/01/geometric_representation_theor_= 18.html =20 Best regards Rafael Borowiecki