[TYPES] Book on Category Theory

[Dan Doel]

I'm not sure which books go into much detail about covariance and
contravariance. I think typically it might be mentioned in connection with
functors and opposite categories, and then it's probably assumed it's
rather 'obvious' from there.

You should know, though, that "anamorphism" and "catamorphism," aren't
terms that originate from category theory, though. They were coined (as far
as I know) in the paper, "Functional Programming with Bananas, Lenses,
Envelopes and Barbed Wire." That paper applies some category theory to
programming, but the terminology like, "catamorphism," is not part of
what's borrowed. And I wouldn't be surprised if most mathematicians had
never heard those terms.

The most directly related book to that stuff that I've read is Pierce's
book, which works up to initial algebras of functors and Lambek's lemma.
But I don't think you'll find "catamorphism" there, either, even though
it's written by and for the sort of person who might actually encounter the
Banana paper.

-- Dan

On Mon, Oct 23, 2017 at 10:56 AM, Aaron Gray <aaronngray.lists at gmail.com>
wrote:

> [ The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list
> ]
>
> Thanks everyone, but as far as I can tell none of these books give me any
> real stuff on covariance, contravariance, anamophisms and catamophisms.
>
> On 19 October 2017 at 16:59, John Leo <leo at halfaya.org> wrote:
>
> > I agree Pierce's book is great, and my favorite overall reference Awodey
> > also has some material on applications to type theory.
> >
> > For specific connections, the best sources are probably lecture notes for
> > various summer school courses.  My three favorites are those in the
> > "Category Theory and Functional Programming" section of this page:
> > https://github.com/halfaya/BayHac/blob/master/references.md
> >
> > John
> >
> >
> >
> > On Thu, Oct 19, 2017 at 2:50 AM, Moez A. AbdelGawad <moez at cs.rice.edu>
> > wrote:
> >
> >> [ The Types Forum, http://lists.seas.upenn.edu/ma
> >> ilman/listinfo/types-list ]
> >>
> >> In addition to Pierce's book, which was earlier mentioned, I strongly
> >> recommend Spivak's Category Theory for The Sciences and Lawvere &
> >> Schanuel's Conceptual Mathematics. Even though neither book is
> specifically
> >> for computer scientists, but both books are more modern, very
> accessible,
> >> and frequently discuss CS applications.
> >>
> >> -Moez
> >>
> >> -------- Original message --------
> >> From: Aaron Gray <aaronngray.lists at gmail.com>
> >> Date: 18/10/2017  21:22  (GMT+02:00)
> >> To: The TYPES forum <types-list at lists.seas.upenn.edu>
> >> Subject: [TYPES] Book on Category Theory
> >>
> >> [ The Types Forum, http://lists.seas.upenn.edu/ma
> >> ilman/listinfo/types-list ]
> >>
> >> I am looking for a book on Category Theory that is ideally either aimed
> at
> >> Type Theory or has the relevant topics to support the area.
> >>
> >> I have bought three books on the topic so far, one 'Categories for
> Typesw'
> >> by Crole did not even cover covariance and contravariance.I would also
> >> like
> >> coverage of monoid and monads, and morphisms like anamorphisms and
> >> catamorphisms.
> >>
> >> I am also interested in papers applying category theory to areas of type
> >> theory.
> >>
> >> Suggestions of either online or printed material would be appreciated.
> >>
> >> Many tahnks in advance,
> >> --
> >> Aaron Gray
> >>
> >> Independent Open Source Software Engineer, Computer Language Researcher,
> >> Information Theorist, and amateur computer scientist.
> >>
> >
> >
>
>
> --
> Aaron Gray
>
> Independent Open Source Software Engineer, Computer Language Researcher,
> Information Theorist, and amateur computer scientist.
>