From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/264 Path: news.gmane.org!not-for-mail From: Hugo.BACARD@unice.fr Newsgroups: gmane.science.mathematics.categories Subject: Classifying Space... Date: Thu, 23 Apr 2009 14:02:59 +0200 Message-ID: Reply-To: Hugo.BACARD@unice.fr 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 1240500770 26002 80.91.229.12 (23 Apr 2009 15:32:50 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 23 Apr 2009 15:32:50 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Thu Apr 23 17:34:10 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 1Lx0w6-0008FT-Tu for gsmc-categories@m.gmane.org; Thu, 23 Apr 2009 17:34:03 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Lx0AT-0001Ii-EY for categories-list@mta.ca; Thu, 23 Apr 2009 11:44:49 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:264 Archived-At: Dear category theorists, Sorry for my following stupid questions , but i would like: -Given a monoidal category M , for first assumed to be strict, What kind = of thing do we obtain when we take it's classifying space ?: we take the ner= ve of M and then realising the simplicial sets obtained=20 Explicitely there are theses questions : 1) Does the nerve of M "preserve" (or "reflect") the monoidal structure = of M ? -Is it a monoid in the category of simplicial sets ?=20 -If yes , can we have conditions on a monoid of sSet to be the nerve = of a monoidal category ? I mean, does some kind of "segal condition" ? 2) And What kind of topological spaces of the realization of the nerve -Is it a topological monoid , with some extra structure ?=20 3) And what hapen if M is not strict, or is symmetric, or braided , etc..= .=20 Thank you and sorry if these are completely stupid questions=20