From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2327 Path: news.gmane.org!not-for-mail From: Ronnie Brown Newsgroups: gmane.science.mathematics.categories Subject: Re: Function composition of natural transformations? Date: Wed, 4 Jun 2003 21:53:51 +0100 (BST) Message-ID: References: <20030603203247.GB5160@math-rs-n01.ucr.edu> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018577 3570 80.91.229.2 (29 Apr 2009 15:22:57 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:22:57 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Jun 5 16:12:12 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 05 Jun 2003 16:12:12 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19O06b-0007Ow-00 for categories-list@mta.ca; Thu, 05 Jun 2003 16:08:57 -0300 X-X-Sender: mas010@publix In-Reply-To: <20030603203247.GB5160@math-rs-n01.ucr.edu> Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 18 Original-Lines: 58 Xref: news.gmane.org gmane.science.mathematics.categories:2327 Archived-At: It may be useful to recall the Ehresmann method of setting up the exponential law for categories using the double categoy of commuting squares in a category. This is also written up in (R.Brown, P. NICKOLAS), ``Exponential laws for topological categories, groupoids and groups and mapping spaces of colimits'', {\em Cah. Top. G\'eom. Diff.} 20 (1979) 179-198. The nice point is that the category structure is induced by a double category composition, and so if you have extra structure, such as a topology, that carries over. Ronnie Brown On Tue, 3 Jun 2003, Toby Bartels wrote: > Steve Vickers wrote: > > >It is also possible to use a 2-dimensional syntax, in which horizontal > >composition is composed horizontally and vertical composition is > >composed vertically. Then algebraic manipulations are a bit like sliding > >tiles around in a tray. > > Of course this can be done using big diagrams. > But is there a tight syntax for this just using text? > Can you point to an example? (preferably a TeX source online, > but a printed page in a regular journal would also work). > > > -- Toby > > > Prof R. Brown, School of Informatics, Mathematics Division, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382681 fax: +44 1248 361429 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ (Links to survey articles: Higher dimensional group theory Groupoids and crossed objects in algebraic topology) Centre for the Popularisation of Mathematics Raising Public Awareness of Mathematics CDRom Symbolic Sculpture and Mathematics: http://www.cpm.informatics.bangor.ac.uk/centre/index.html