Re: Applications of (higher) category theory to computer science
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
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (3)
-
Dee Roytenberg -
Fred E.J. Linton -
Urs Schreiber