From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4496 Path: news.gmane.org!not-for-mail From: Michael Shulman Newsgroups: gmane.science.mathematics.categories Subject: symmetric monoidal traces Date: Tue, 19 Aug 2008 19:23:03 -0500 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1241019982 13572 80.91.229.2 (29 Apr 2009 15:46:22 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:46:22 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Aug 19 22:03:32 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 19 Aug 2008 22:03:32 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KVc6e-0004oO-LH for categories-list@mta.ca; Tue, 19 Aug 2008 22:03:24 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 31 Original-Lines: 24 Xref: news.gmane.org gmane.science.mathematics.categories:4496 Archived-At: Hi all, Can someone please point me to whatever categorical references exist regarding the canonical trace for dualizable objects in a symmetric monoidal category? I am particularly interested in (1) elementary expositions accessible to non-category-theorists and (2) any proofs of its uniqueness subject to various conditions. I know there are many references on traced monoidal categories, particularly with applications to computer science, but right now I am only interested in the symmetric monoidal trace. I also know that there are various reinventions/expositions of the notion in, for example, the topological literature (e.g. Dold-Puppe), but I would like an exposition not tied to any particular application. Finally, I know that the Joyal-Street-Verity paper "Traced Monoidal Categories" proves that the canonical symmetric (or, more precisely, balanced) monoidal trace is "universal" in that any traced monoidal category can be embedded in one equipped with the canonical trace, but as far as I can tell this need not determine the canonical trace uniquely. Thanks!! Mike