From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6054 Path: news.gmane.org!not-for-mail From: soloviev@irit.fr Newsgroups: gmane.science.mathematics.categories Subject: Re: "Databases are Categories" Date: Wed, 18 Aug 2010 08:14:58 +0200 (CEST) Message-ID: References: Reply-To: soloviev@irit.fr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset=utf-8 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1282215794 6129 80.91.229.12 (19 Aug 2010 11:03:14 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 19 Aug 2010 11:03:14 +0000 (UTC) Cc: "Zinovy Diskin" , categories@mta.ca To: "David Spivak" Original-X-From: majordomo@mlist.mta.ca Thu Aug 19 13:03:11 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Om2tr-0007gn-1n for gsmc-categories@m.gmane.org; Thu, 19 Aug 2010 13:03:11 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:43685) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Om2sD-0002Bv-7u; Thu, 19 Aug 2010 08:01:29 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Om2sA-0008K0-Gn for categories-list@mlist.mta.ca; Thu, 19 Aug 2010 08:01:26 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6054 Archived-At: Hi, then , in this setting, how coherence should be interpreted? According to Mac Lane, a coherence theorem asserts commutativity of a class of diagrams; some other authors mean rather decision procedure/criteria for commutativity of diagrams. By the way, did you consider some kind of "basic" arrows and generated "canonical maps"? Do there appear/be used some known types of categories with structure (cartesian, monoidal, cartesian closed, monoidal closed)? Another interesting question could be isomorphism of objects. Best wishes Sergei Soloviev Hi all, > > The basic idea of my talk was this: one can think of any category C as = a > "database schema": the objects of C are called "tables" and an arrow > f:A-->B > is called a "column of table A with values in table B". Now a functor > C-->Sets is a "state" of that database: it fills every table with a set= of > rows. Leaf objects of C (objects with no outgoing arrows) correspond t= o > "pure data." One can thus visualize a category as a system of tables; > commutative diagrams correspond to "rules" such as "the secretary of a > department must be in that department." > > Using sketches instead of categories allows a little more flexibility, = but > the basic idea is as above. The model is nice for a variety of reasons= , > most of all its simplicity. In polite contradiction to one of Diskin's > claims, two database administrators (at two large multi-national > corporations) that I know think it is a viable model. They do not balk= at > the idea of data columns being considered as foreign keys. It puts > everything on the same playing field. > ... [For admin and other information see: http://www.mta.ca/~cat-dist/ ]