From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1204 Path: news.gmane.org!not-for-mail From: Gaunce Lewis Newsgroups: gmane.science.mathematics.categories Subject: looking for references Date: Fri, 27 Aug 1999 16:01:06 -0400 Message-ID: <4.2.0.58.19990827154835.00987a70@ichthus.syr.edu> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Trace: ger.gmane.org 1241017635 29935 80.91.229.2 (29 Apr 2009 15:07:15 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:07:15 +0000 (UTC) Cc: rdp@imada.sdu.dk To: Categories list Original-X-From: cat-dist Fri Aug 27 18:54:17 1999 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id RAA12945 for categories-list; Fri, 27 Aug 1999 17:41:39 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: lglewis@ichthus.syr.edu X-Mailer: QUALCOMM Windows Eudora Pro Version 4.2.0.58 Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 26 Xref: news.gmane.org gmane.science.mathematics.categories:1204 Archived-At: A colleague in geometric topology has encountered a categorical construction for which he would like some literature references. He has asked me to pass this request on to this mailing list. Roughly speaking, the construction takes a category carrying an action by a monoid and forms an associated "orbit" category. However, rather than identifying objects in the same orbit, it inserts a canonical isomorphism between them. Here are the details: Let M be a monoid which is also a poset. Assume that the multiplication on M preserves the order and that the unit u for the multiplication on M is an initial element for the poset. Think of M as a category with morphisms derived from the poset structure. Let C be any category and let F : M x C -> C be a functor which gives an action of M on C. For each m in M and each c in C, there is a map t(m,c) from c to F(m,c) obtained by applying F to the poset relation u \leq m and the identity map on c. Form the category of fractions of C in which all the maps t(m,c) have been inverted. Note that it looks somewhat like the orbit category C/M, but with the objects in the same orbit linked by canonical isomorphisms (derived from the t(m,c)) rather than identified. Has anyone seen this construction before? Is there literature on it? Thanks for any help on this, Gaunce Lewis