From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2416 Path: news.gmane.org!not-for-mail From: Ross Street Newsgroups: gmane.science.mathematics.categories Subject: Rider to my response to Jean Benabou Date: Thu, 21 Aug 2003 12:13:27 +1000 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" ; format="flowed" X-Trace: ger.gmane.org 1241018643 4052 80.91.229.2 (29 Apr 2009 15:24:03 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:24:03 +0000 (UTC) To: categories@mta.ca, jean benabou Original-X-From: rrosebru@mta.ca Thu Aug 21 15:02:57 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 21 Aug 2003 15:02:57 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19ptiA-0006ne-00 for categories-list@mta.ca; Thu, 21 Aug 2003 14:59:02 -0300 X-Sender: street@icsmail.ics.mq.edu.au Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 8 Original-Lines: 28 Xref: news.gmane.org gmane.science.mathematics.categories:2416 Archived-At: Dear Jean After seeing both Brian and Max in the last two days, I would like to add two remarks to my last message. 1) Brian pointed out that you did not ask for your base V to be closed which is assumed in his paper in SLNM137. However, this is not really a restriction: just embed V in its presheaves with convolution closed monoidal structure. 2) Max reminded me of his old result (not in the LaJolla Proceedings, but known soon after) that a monoidal V-category is none other than a monoidal category W with a "normal" monoidal functor W --> V. (Normal here means that the unit is preserved.) I think this was mentioned by Max somewhere in the literature but I cannot remember where; possibly SLNM420. The good thing about it is that V-categories enriched in the monoidal V-category W turn out to be mere W-categories. An example is the monoidal category W = DGAb of chain complexes of abelian groups; it can be regarded as a monoidal additive category (that is, enriched in abelian groups V = Ab) or as a mere monoidal category; categories enriched in the latter are automatically additive. Best wishes, Ross