Categories in real world applications
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 ------------------------- mobile +46 70 586 4414 website www8.cs.umu.se/~peklund [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Well in my limited knowledge I can say that a lot of category theory had been employed in order to design many constructions for programming languages. For instance in Haskell the notion of category, functor and monads are used as typeclasses in order to abstract some general pattern lurking around in many parametric types. So from this perspective category theory gives to (real world) programmers some tools to produce abstract-reusable-patterns, to code and avoid boilerplate. There is also Spivak's program to treat database categorically: yeah I know this is research, nonetheless it has to do with modelling real world objects (database) and modelling data is part (if not the essence) of real world application of mathematics. There are also other researcher that are trying to find categorical models for real world objects (see Baez's work for instance). I don't know if these works are yet ready for real world applications, but they seems promising. Hope this helps. On Tue, Feb 02, 2016 at 07:10:09AM +0200, 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
-------------------------
mobile +46 70 586 4414 website www8.cs.umu.se/~peklund
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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
-------------------------
mobile +46 70 586 4414 website www8.cs.umu.se/~peklund
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
In response to Patrick Eklund Among the real-world applications of category theory, I can mention those deduced from the categorical-based methodology of "Memory Evolutive Systems" which we have been developing with Jean-Paul Vanbremeersch for the last 30 years . MES propose a model for studying evolutionary multi-scale, multi-agent systems such as biological and social systems. The main theory can be found in our Elsevier book: "Memory Evolutive Systems: Hierarchy, Emergence, Cognition" (2007), and more recent results in a series of papers (cf. the references on my site http://ehres.pagesperso-orange.fr (or on Research Gate at my name Andree Ehresmann). In particular MES lead to realworld applications in: - Biology and Medecine (e.g. aging theory for an organism), - Neurosciences: model MENS studying the development of higher cognitive processes, up to consciousness, and creativity, - Anticipation and future studies, - Innovation and design. Best regards, Andree [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Dear Prof Erklund, The usefulness of category theory is best seen in mathematics. Mathematics is part of the real world. Category theory has applications to algebra, geometry, topology, homotopy theory, algebraic-topology, algebraic-geometry, number theory, combinatorics, logic, etc. -A ________________________________________ From: Patrik Eklund [peklund@cs.umu.se] Sent: Tuesday, February 02, 2016 12:10 AM To: Categories Subject: categories: Categories in real world applications 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 ------------------------- mobile +46 70 586 4414 website www8.cs.umu.se/~peklund [For admin and other information see: http://www.mta.ca/~cat-dist/ ] [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (5)
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Andree EHRESMANN -
Bob Coecke -
Giorgio Mossa -
Joyal, André -
Patrik Eklund