From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/265 Path: news.gmane.org!not-for-mail From: Oleksandr Manzyuk Newsgroups: gmane.science.mathematics.categories Subject: Re: Preprint available: Close categories vs. closed multicategories Date: Thu, 23 Apr 2009 00:53:13 -0400 Message-ID: Reply-To: Oleksandr Manzyuk NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1240500783 26050 80.91.229.12 (23 Apr 2009 15:33:03 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 23 Apr 2009 15:33:03 +0000 (UTC) To: pratt@cs.stanford.edu, categories@mta.ca Original-X-From: categories@mta.ca Thu Apr 23 17:34:22 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 1Lx0wQ-0008Lx-Dj for gsmc-categories@m.gmane.org; Thu, 23 Apr 2009 17:34:22 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Lx097-0001Al-Am for categories-list@mta.ca; Thu, 23 Apr 2009 11:43:25 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:265 Archived-At: Dear Vaughan, > Very interesting definition. =C2=A0Do you have an example of a closed cat= egory > that cannot be expanded to a closed monoidal category? =C2=A0If there's o= ne in > your paper then my apologies for overlooking it. Every closed category can be embedded fully faithfully into a closed monoidal category such that the closed structure is preserved; this is due to Laplaza (exact reference in my paper). However, non-monoidal closed categories do occur. I was motivated by the example of A-infinity categories, and frankly, I am not aware of any other non-trivial and non-artificial examples, but I am sure there must be some, it is just my ignorance. Best, Oleksandr --=20 "Dealing with failure is easy: Work hard to improve. Success is also easy to handle: You've solved the wrong problem. Work hard to improve." - Alan Perlis