From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8813 Path: news.gmane.org!not-for-mail From: Bob Coecke Newsgroups: gmane.science.mathematics.categories Subject: Re: Categories in real world applications Date: Tue, 2 Feb 2016 18:45:56 +0000 Message-ID: References: Reply-To: Bob Coecke NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Apple Message framework v1283) Content-Type: text/plain; charset=windows-1252 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1454511925 9326 80.91.229.3 (3 Feb 2016 15:05:25 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 3 Feb 2016 15:05:25 +0000 (UTC) Cc: Bob Coecke , Categories To: Patrik Eklund Original-X-From: majordomo@mlist.mta.ca Wed Feb 03 16:05:16 2016 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.7.22]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1aQyzb-0006Cs-2m for gsmc-categories@m.gmane.org; Wed, 03 Feb 2016 16:05:15 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:51488) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1aQyyn-00064p-Td; Wed, 03 Feb 2016 11:04:25 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1aQyyi-000575-19 for categories-list@mlist.mta.ca; Wed, 03 Feb 2016 11:04:20 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8813 Archived-At: Hi, for a couple of years now, we have been using categories to relate = grammatical structure (eg Lambek calculus/pregroups) to meaning spaces = used in natural language processing eg vector spaces. The interface of = interaction is properly categorical. The best analogy would be that = while a TQFT functorially maps topology change on linear maps, here = grammatical reduction is mapped on composition of meanings, yielding an = algorithm that computes meanings of phrases and sentences from meaning = of parts. This method has outperformed other ones in NLP. Here are = some refs:=20 B. Coecke, M. Sadrzadeh, and S. Clark. Mathematical foundations for a = compositional distributional model of meaning. arXiv:1003.4394, 2010. E. Grefenstette and M. Sadrzadeh. Experimental support for a categorical = compositional distributional model of meaning. In Proceedings of the = Conference on Empirical Methods in Natural Language Processing, EMNLP = =9211, pages 1394=961404, Stroudsburg, PA, USA, 2011. ACL. Sadrzadeh, S. Clark, and B. Coecke. The Frobenius anatomy of word = meanings I: subject and object relative pronouns. Journal of Logic and = Computation, page ext044, 2013. arXiv:1404.5278 On 2 Feb 2016, at 05:10, Patrik Eklund wrote: > If you know of any real world applications of category theory, please > let me know. I would be interested to know of clearly described > applications rather that anticipated ones using categories in = background > theories. >=20 > When we speak about "applications of categories" or "applied = categories" > we mostly or almost exclusively mean applying categories within > mathematics (or theoretical computer science), where we have = categories > in algebra, topology, logic (and type theory), and so on. We do have > real world applications of algebra, topology, logic, and many other > branches of mathematics, but possible use of categories is then hidden > and/or indirect. >=20 > Therefore the question: Are categories applicable in the real world? >=20 > Application areas could be found within the public or private sectors. > In the public sector it can be e.g. within education and health, and = in > the private sector in can be e.g. within energy, finance and > manufacturing. >=20 > If I receive more than just a few replies, I will make a survey of it, > and later on inform the mailing list about the survey. >=20 > Looking forward. >=20 > Best, >=20 > Patrik >=20 >=20 >=20 > --=20 > Prof. Patrik Eklund > Ume?? University > Department of Computing Science > SE-90187 Ume?? > Sweden >=20 > ------------------------- >=20 > mobile +46 70 586 4414 > website www8.cs.umu.se/~peklund >=20 >=20 > [For admin and other information see: http://www.mta.ca/~cat-dist/ ] [For admin and other information see: http://www.mta.ca/~cat-dist/ ]