Re: Categories in real world applications

[Bob Coecke <bob.coecke@cs.ox.ac.uk>]

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: 

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 ’11, pages 1394–1404, 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.
> 
> 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.
> 
> Therefore the question: Are categories applicable in the real world?
> 
> 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.
> 
> 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.
> 
> Looking forward.
> 
> Best,
> 
> Patrik
> 
> 
> 
> -- 
> Prof. Patrik Eklund
> Ume?? University
> Department of Computing Science
> SE-90187 Ume??
> Sweden
> 
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