Categories in real world applications

Categories in real world applications

[Patrik Eklund]

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/ ]

Re: Categories in real world applications

[Giorgio Mossa]

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/ ]

Re: Categories in real world applications

[Bob Coecke]

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/ ]

Re: Categories in real world applications

[Andree EHRESMANN]

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/ ]

RE: Categories in real world applications

[Joyal, André]

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/ ]