From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4382 Path: news.gmane.org!not-for-mail From: David Roberts Newsgroups: gmane.science.mathematics.categories Subject: Strictifying monoidal functors Date: Wed, 7 May 2008 16:29:08 +0930 Message-ID: NNTP-Posting-Host: main.gmane.org Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019910 13039 80.91.229.2 (29 Apr 2009 15:45:10 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:45:10 +0000 (UTC) To: Categories list Original-X-From: rrosebru@mta.ca Wed May 7 09:42:35 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 07 May 2008 09:42:35 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1JtitD-0000AH-Px for categories-list@mta.ca; Wed, 07 May 2008 09:36:55 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 5 Original-Lines: 22 Xref: news.gmane.org gmane.science.mathematics.categories:4382 Archived-At: Hi all, While we can make all monoidal categories strict, I was wondering how strict we can make monoidal functors. More precisely, given a strong monoidal functor F:(C,@,I) --> (D,*,1) between strict monoidal categories, it has the data m_xy: F(x)*F(y) ---> F(x@y) (natural) u:1 ---> F(I). Is F naturally isomorphic to a strong monoidal functor such that u is the identity? In Baez-Lauda HDA 5 it is an exercise to the reader in the proof of Proposition 8.3.6 to do this for weak monoidal categories. Cheers, David