From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4901 Path: news.gmane.org!not-for-mail From: Steve Vickers Newsgroups: gmane.science.mathematics.categories Subject: Re: patenting colimits? Date: Wed, 27 May 2009 17:08:29 +0100 Message-ID: Reply-To: Steve Vickers NNTP-Posting-Host: lo.gmane.org Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1243483341 20449 80.91.229.12 (28 May 2009 04:02:21 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 28 May 2009 04:02:21 +0000 (UTC) To: Toby Bartels , categories@mta.ca Original-X-From: categories@mta.ca Thu May 28 06:02:19 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 1M9Wop-0007BG-06 for gsmc-categories@m.gmane.org; Thu, 28 May 2009 06:02:15 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1M9WFM-0000qZ-Rq for categories-list@mta.ca; Thu, 28 May 2009 00:25:36 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4901 Archived-At: Toby Bartels wrote: > ... > Certainly much of what is in the patent application is obvious, > but perhaps not all of it; were these diagrams of diagrams a new idea?, > or was applying them to computer system specifications a new idea?. > ... Dear Toby, The idea of treating specifications as colimits is a few decades old now. Burstall and Goguen used it in their categorical account of their specification language Clear, with a specification used to construct a new theory as colimit of others. The hierarchical step, diagrams of diagrams, was studied by Catherine Oriat in her thesis and (I believe) a TCS paper in 2000. My own student Gillian Hill investigated a variant of this (PhD Thesis 2002; also two papers with me, 2001, 2006), replacing the category of finite diagrams over a base category C by the equivalent category of finitely presented presheaves. Both are finite cocompletions, but a presheaf presentation by generators and relations comes over neatly as a "configuration by components and sharing". For obvious reasons the iterated construction "flattens" back down to the single one (the construction is a KZ-monad in the 2-category of categories). Gillian also investigated a multi-level configuration language that maintains the hierarchical structure without flattening (configurations of configurations of configurations of ...) and includes cross-level specification morphisms. However, we did not persevere to work out the categorical semantics of this, nor did we make a computer implementation. Regards, Steve Vickers. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]