Applications of (higher) category theory to computer science

Applications of (higher) category theory to computer science

[Dee Roytenberg]

Dear colleagues,

Could someone recommend a good text on the subject? I am aware of the book
by Barr and Wells; however, unlike that book, which is intended for
computer scientists who want to learn category theory, I am looking for
something, in a way, opposite: a source for those who know category theory
but not much of computer science.

Many thanks in advance.

- Dee


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Re: Applications of (higher) category theory to computer science

[Harley Eades III]

Hi, Dee.

On Dec 11, 2014, at 8:38 AM, Dee Roytenberg <roytenberg.d@gmail.com> wrote:

> Dear colleagues,
> 
> Could someone recommend a good text on the subject? I am aware of the book
> by Barr and Wells; however, unlike that book, which is intended for
> computer scientists who want to learn category theory, I am looking for
> something, in a way, opposite: a source for those who know category theory
> but not much of computer science.

I can recommend the following books:

“Categorical Logic and Type Theory” by Bart Jacobs
http://www.cs.ru.nl/B.Jacobs/CLT/bookinfo.html

“Categories for Types” by Roy Crole
http://www.amazon.com/Categories-Studies-Emotion-Social-Interaction/dp/0521450926

Both of these are related to the study of type theory — and logic — which can be seen as a 
logical foundation to functional programming.  So not in terms of CS in general.

The following is another “introduction” to category theory, but has lots of examples:
“Categories for Computer Science” by R. F. C. Walters

http://www.amazon.com/Categories-Computer-Science-Cambridge-Texts/dp/0521422264

These are all the ones I can think of right now.  I am interested in what others have to
offer.  I have not found much in the way of books covering a wide spectra of CS, but
rather only specialties. 

Very best,
.\ Harley

> 
> Many thanks in advance.
> 
> - Dee
> 
> 
> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]



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Re: Applications of (higher) category theory to computer science

[Kyle Marek-Spartz]

It's not a book, but the Typeclassopedia, particularly the instances
sections, might be relevant:

https://www.haskell.org/haskellwiki/Typeclassopedia

Dee Roytenberg writes:

> Dear colleagues,
>
> Could someone recommend a good text on the subject? I am aware of the book
> by Barr and Wells; however, unlike that book, which is intended for
> computer scientists who want to learn category theory, I am looking for
> something, in a way, opposite: a source for those who know category theory
> but not much of computer science.
>
> Many thanks in advance.
>
> - Dee
>
>
> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

--
Kyle Marek-Spartz


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Re: Applications of (higher) category theory to computer science

[Dee Roytenberg]

Many thanks to everyone who replied, with enough suggestions to fill a
bookshelf!

On Thu, Dec 11, 2014 at 4:45 PM, Kyle Marek-Spartz
<kyle.marek.spartz@gmail.com> wrote:
> It's not a book, but the Typeclassopedia, particularly the instances
> sections, might be relevant:
>
> https://www.haskell.org/haskellwiki/Typeclassopedia
>
> Dee Roytenberg writes:
>
>> Dear colleagues,
>>
>> Could someone recommend a good text on the subject? I am aware of the book
>> by Barr and Wells; however, unlike that book, which is intended for
>> computer scientists who want to learn category theory, I am looking for
>> something, in a way, opposite: a source for those who know category theory
>> but not much of computer science.
>>
>> Many thanks in advance.
>>
>> - Dee
>
> --
> Kyle Marek-Spartz

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Re: Applications of (higher) category theory to computer science

[Urs Schreiber]

On 12/11/14, Dee Roytenberg <roytenberg.d@gmail.com> wrote:

> Many thanks to everyone who replied, with enough suggestions to fill a
> bookshelf!


Just to add one remark: while there is a lot of literature this
relation, at the heart of it there is one single simple but profound
dictionary which translates

  category theory <-> type theory <-> computation

such that these three subjects become, essentially, just three
different faces of one single phenomenon.

Since this is so neat, Bob Harper once referred to this as
"computational trinitarianism".

A hyperlinked version of the dictionary, with further pointers, is here:

   http://ncatlab.org:8080/nlab/show/computational+trinitarianism

Best,
Urs


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RE: Applications of (higher) category theory to computer science

[Linton, Fred]

Dee Roytenberg [roytenberg.d@gmail.com], on Thursday, December 11, 2014, asked, regarding Applications of (higher) category theory to computer science:

> Could someone recommend a good text on the subject? ...

I might suggest Category Theory applied to Computation and Control, Proceedings of the First International Symposium, U. Mass., Amherst, 1974, ed. E.G. Manes, and the works by Arbib & Manes, and by Goguen, Thatcher, Wright, et al., cited in bibliographies within those proceedings articles.

I hope that helps. Cheers, -- FEJ

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RE: Applications of (higher) category theory to computer science

[Kyle Marek-Spartz]

The Arbib & Manes text I've got (Arrows, Structures, & Functors) is a
good intro to category theory, and doesn't dive into how it applies to
computer science, as much as I would hope.

I haven't read it, but I'd imagine e.g. Algebraic Approaches to Program
Semantics might be more appropriate.




Linton, Fred writes:

> Dee Roytenberg [roytenberg.d@gmail.com], on Thursday, December 11, 2014, asked, regarding Applications of (higher) category theory to computer science:
>
>> Could someone recommend a good text on the subject? ...
>
> I might suggest Category Theory applied to Computation and Control, Proceedings of the First International Symposium, U. Mass., Amherst, 1974, ed. E.G. Manes, and the works by Arbib & Manes, and by Goguen, Thatcher, Wright, et al., cited in bibliographies within those proceedings articles.
>
> I hope that helps. Cheers, -- FEJ

--
Kyle Marek-Spartz


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RE: Applications of (higher) category theory to computer science

[Fred E.J. Linton]

Another suggestion regarding Dee Roytenberg's request for

>> ... a good text on the subject [Applications of (higher) 
>> category theory to computer science]? ...
  
in addition to 

> Category Theory applied to Computation and Control, ... 1974, ... :

there's also perhaps David Spivak's very 21st century Category Theory for
the Sciences, ISBN 978-0-262-02813-4, MIT Press, 2014. Very little actual
category theory, apart from definitions, examples and illustrations, but 
it's exactly those examples and illustrations (taken from computer science, 
from sociology, from physics, from biology, from operations research, etc.) 
that may be what the OP is seeking.

Be aware that, in this book's presentation, Yoneda's Lemma finally turns 
up somewhat past page 400 (of 486 pp. total), and, for its proof (which I
guess lies beyond the scope of Spivak's book), the reader is referred 
to Mac Lane's Categories for the Working Mathematician :-) .

Cheers, -- Fred



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