From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6050 Path: news.gmane.org!not-for-mail From: Zinovy Diskin Newsgroups: gmane.science.mathematics.categories Subject: Re: Re: "Databases are Categories" Date: Mon, 16 Aug 2010 12:07:40 -0400 Message-ID: References: Reply-To: Zinovy Diskin 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 1282002194 16133 80.91.229.12 (16 Aug 2010 23:43:14 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 16 Aug 2010 23:43:14 +0000 (UTC) Cc: categories@mta.ca To: =?UTF-8?Q?Mattias_Wikstr=C3=B6m?= Original-X-From: majordomo@mlist.mta.ca Tue Aug 17 01:43:12 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Ol9Kh-00049P-Ct for gsmc-categories@m.gmane.org; Tue, 17 Aug 2010 01:43:11 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:38960) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Ol9JC-0001Ft-GL; Mon, 16 Aug 2010 20:41:38 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Ol9J9-0007XW-HT for categories-list@mlist.mta.ca; Mon, 16 Aug 2010 20:41:35 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6050 Archived-At: 2010/8/14 Mattias Wikstr=C3=B6m : > I think it makes sense to regard database schemas as theories and > databases as models of such theories. Given a theory T that models yes, this is the basic underlying assumption in a series of papers of Michael Johnson and the moderator of this list. > some database schema S, a term in the language of T may be thought of > as a "database query" (to obtain the result of the query, simplify the > term), a query is a formula (defining a derived table) rather than a term while a statement that two terms in the language of T are equal > may be thought of as a "database constraint" that one may want to add > to S. there are many types of non-equational constraints, for example, inclusion P=3D>Q with P,Q formulas > > What sort of theory should a database schema be? This surely depends > on what exactly one is trying to model: A schema in Company A's DBMS > (database management system) is rarely the same thing as a schema in > Company B's DBMS, and in any case one probably wants to work with some > idealised mathematical model. > a good question is what the place of SQL on the scale of logical doctrines is. Since models of SQL-theories include predefined infinite domains with operations (think of Integer and String), and finite domains for tables, model theory for SQL is not classical. I'm not sure but it seems model-theorists call it "metafinite model theory" (Gradel and Gurevich). > David Spivak seems to offer two different answers. On the one hand, a > database schema may be the same thing as a category. On the other > hand, a database schema may be a labeled simplicial set. Both answers > may be found at http://www.uoregon.edu/~dspivak/cs/ . > I took a look at the slides of "databases are categories" talk. It seems to be an overly simplified model. Since an employee may work for several or none departments, data should be modeled by a functor into Rel rather than Set. 2-category structure may be important, and we often have a lax functor F(a;b) ---------------------------------------- >> Date: Mon, 9 Aug 2010 11:12:34 -0500 >> Subject: categories: "Databases are Categories" (again) >> From: vigalchin@gmail.com >> To: categories@mta.ca >> >> Hello, >> >> I stumbled across this tech talk: >> http://www.galois.com/blog/2010/05/27/tech-talk-categories-are-databases= / I >> was wondering >> what others in this mail list think about Spivak's thesis. I apologize i= f >> already posted. >> >> >> Regards, >> >> Vasili >> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]