From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5493 Path: news.gmane.org!not-for-mail From: "Serge P. Kovalyov" Newsgroups: gmane.science.mathematics.categories Subject: Super comma category Date: Thu, 7 Jan 2010 19:33:39 +0600 (NOVT) Message-ID: References: <20090218222112.L22481@mx.nsc.ru> Reply-To: "Serge P. Kovalyov" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1262917851 703 80.91.229.12 (8 Jan 2010 02:30:51 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 8 Jan 2010 02:30:51 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Fri Jan 08 03:30:44 2010 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 1NT4cd-0001sz-MM for gsmc-categories@m.gmane.org; Fri, 08 Jan 2010 03:30:43 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NT4CF-0003VP-M2 for categories-list@mta.ca; Thu, 07 Jan 2010 22:03:27 -0400 In-Reply-To: <20090218222112.L22481@mx.nsc.ru> Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5493 Archived-At: Dear Category Theory gurus, Is there any literature in which MacLane's "super comma category" (Cat./.C) of all small diagrams in a category C is studied in details? Actually I work in its covariant form, where a morphism from a diagram D:X->C to G:Y->C is a pair (e,F) consisting of a functor F:X->Y and a natural transformation e:D->GF. For example, is it known that the embedding of an ordinary comma category Cat/C into Cat./.C preserves colimits? Also there exists a monad (Cat./.-, d, m) on CAT, where d_C takes each C-object X to a discrete diagram {X}, and m represents "drawing" a diagram of diagrams as a diagram. Is its Eilenberg-Moore category isomorphic to some "familiar" construction? Thanks, Serge. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]