[TYPES] Book on Category Theory

[Gabriel Scherer]

Hi Aaron,

I think you may misunderstand what "category theory for type theory" is
about and its focus area. It is perfectly natural for an outsider to be a
bit confused about the topic you want to learn about (that's the point of
learning), but my impression is that you have some work to do find out what
you actually want before you can usefully tap types-list as a direct
citation source. Maybe some people around here can help you do this
unraveling work (Sean Leather's last reference seems to go in the same
direction), but otherwise there are other places where people may be more
knowledgeable about orienting people living in the gap between "category
theory keywords I hear when I hang around Haskellers" and "category theory
books", for example https://www.reddit.com/r/haskell/ .

(Reverse engineering what you say, it also sounds like Bartosz Milewski's
book mentioned by François Thiré above may be one of the closer to what you
are looking for.)

On Mon, Oct 23, 2017 at 4:56 PM, 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.
>