From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/251 Path: news.gmane.org!not-for-mail From: Andreas Holmstrom Newsgroups: gmane.science.mathematics.categories Subject: Re: Smooth and proper functors Date: Wed, 15 Apr 2009 19:44:05 +0100 Message-ID: Reply-To: Andreas Holmstrom NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1239893856 11640 80.91.229.12 (16 Apr 2009 14:57:36 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 16 Apr 2009 14:57:36 +0000 (UTC) To: Hasse Riemann , categories@mta.ca Original-X-From: categories@mta.ca Thu Apr 16 16:58:56 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 1LuT2x-0002Jt-O6 for gsmc-categories@m.gmane.org; Thu, 16 Apr 2009 16:58:35 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LuSGO-00009Y-4M for categories-list@mta.ca; Thu, 16 Apr 2009 11:08:24 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:251 Archived-At: Hi Rafael, I don't know much about this, but I listened to an excellent talk of Maltsiniotis a few months ago at IHES and posted the scanned notes in a blog post here: http://homotopical.wordpress.com/2009/01/26/maltsinotis-grothendieck-and-homotopical-algebra/ These notes (on page 11-12) contain at least the definition of proper and smooth functors, and the duality statement, so maybe they can be of some limited use. Hopefully other people on this list can provide some more substantial information. Best regards, Andreas Holmstrom 2009/4/15 Hasse Riemann : > > > > Hi category gurus and categorists > > > > I have many questions about category theory but i start with one. > > > > 1> > > What are smooth functors and proper functors, originating in pursuing stacks? > > Both nontechnically and technicaly. > > > > I know they are dual to each other and that they are characterized by cohomological properties > > inspired by the proper or smooth base change theorem in algebraic geometry, but what is the relation? > > (I don't know the statement of the theorems) > > > > Finally, 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? > > > > 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 > > > > Best regards > > Rafael Borowiecki > > >