From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3325 Path: news.gmane.org!not-for-mail From: "John Baez" Newsgroups: gmane.science.mathematics.categories Subject: Re: Hecke eigensheaves and KV 2-vectors Date: Thu, 18 May 2006 08:37:27 -0700 (PDT) Message-ID: <13386.5149495707$1241019230@news.gmane.org> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019230 8247 80.91.229.2 (29 Apr 2009 15:33:50 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:33:50 +0000 (UTC) To: categories@mta.ca (categories) Original-X-From: rrosebru@mta.ca Fri May 19 08:26:55 2006 -0300 X-Keywords: X-UID: 269 Original-Lines: 25 Xref: news.gmane.org gmane.science.mathematics.categories:3325 Archived-At: I wrote: > You're asking about something more general: "weak eigenobjects" of > endofunctors T: C -> C on *monoidal* categories C. In other words: objects > c in C equipped with isomorphisms Tc -> a tensor c for some fixed object > a. Sorry! Actually Urs is asking about an even more general situation. A is a monoidal category, C is a category tensored over A, T: C -> C, and we seek objects c in C equipped with isomorphisms Tc -> a tensor c for some fixed object a. We can form the category of these, which is the pseudo-equalizer of T and a tensor -, and call it an "eigenspace of T". For Urs, A = Vect and C is a Vect-module. Best, jb