From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5172 Path: news.gmane.org!not-for-mail From: Tony Meman Newsgroups: gmane.science.mathematics.categories Subject: Comma categories Date: Thu, 24 Sep 2009 22:23:22 +0200 Message-ID: Reply-To: Tony Meman NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: ger.gmane.org 1253829727 2298 80.91.229.12 (24 Sep 2009 22:02:07 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 24 Sep 2009 22:02:07 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Fri Sep 25 00:02:00 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 1MqwO0-0003lo-8e for gsmc-categories@m.gmane.org; Fri, 25 Sep 2009 00:02:00 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MqvuI-0005uu-ID for categories-list@mta.ca; Thu, 24 Sep 2009 18:31:18 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5172 Archived-At: Dear category theorists, I have two questions concerning comma categories. If C is a category with a terminal object *, is the comma category (C,*) consisting of arrows from C to * isomorphic to the category C itself? If this is true, the same should apply to the dual case with an initial object. The category sSet of simplicial sets is the category of functors from the opposite delta category Delta^op to Set. The category of pointed simplicial sets sSet* is defined as the comma category (delta0, sSet), where delta0=hom(-,[0]). Is sSet* isomorphic to the category of functors from ([0],Delta)^op to Set? Thank you in advance for any help. Tony [For admin and other information see: http://www.mta.ca/~cat-dist/ ]