From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5427 Path: news.gmane.org!not-for-mail From: selinger@mathstat.dal.ca (Peter Selinger) Newsgroups: gmane.science.mathematics.categories Subject: Re: additions Date: Fri, 25 Dec 2009 22:14:16 -0400 (AST) Message-ID: References: Reply-To: selinger@mathstat.dal.ca (Peter Selinger) NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1261923640 3679 80.91.229.12 (27 Dec 2009 14:20:40 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 27 Dec 2009 14:20:40 +0000 (UTC) To: joyal.andre@uqam.ca Original-X-From: categories@mta.ca Sun Dec 27 15:20:33 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 1NOtyz-00033b-BH for gsmc-categories@m.gmane.org; Sun, 27 Dec 2009 15:20:33 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NOtXg-0002G2-Py for categories-list@mta.ca; Sun, 27 Dec 2009 09:52:20 -0400 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5427 Archived-At: In defense of Andre's list, the explanation he gave for his original list was that subjects in category theory become hot from time to time in response to factors such as new developments outside category theory. The list was supposed to be a list of categorical subjects, not a list of the respective developments that have inspired their use and advancement. The current use of category theory in quantum foundations is clearly an interesting development, and has inspired new work in category theory. But I would still be comfortable, for the time being, in classifying this new work as falling within the existing subjects of "monoidal categories" and "category theory and computer science" on Andre's growing list. Recently also "topos theory" due to the work of Andreas Doering, Klaas Landsman, and others on topos models for basic physics. As for the completeness result that Thorsten mentioned, the reference is: M. Hasegawa, M. Hofmann and G. Plotkin, "Finite dimensional vector spaces are complete for traced symmetric monoidal categories". In Pillars of Computer Science: Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday, Springer LNCS 4800, pages 367-385, February 2008. The result is that an equation holds in all traced symmetric monoidal categories if and only if it holds in finite dimensional vector spaces. An immediate corollary is that the analogous result holds for compact closed categories. A simplified proof, and extension to dagger compact closed categories (w.r.t. finite dimensional Hilbert spaces), can be found here: P. Selinger, "Finite dimensional Hilbert spaces are complete for dagger compact closed categories". Extended abstract, to appear in Proceedings of the 5th International Workshop on Quantum Physics and Logic (QPL 2008), Reykjavik, 2010. Merry Christmas to all, -- Peter [For admin and other information see: http://www.mta.ca/~cat-dist/ ]