On Wed, Feb 15, 2012 at 11:38 PM, Joachim Durchholz <j...@durchholz.org> wrote:
> Am 15.02.2012 21:34, schrieb Aaron Meurer:
>
>> Is category theory used outside category theory?
>
>
> It is, in some functional programming languages.
> In Haskell, there's an ADT that is called "monad", and it is supposed to be
> derived from the monads in category theory. Some people are working on
> something that is called an "arrow", which is supposed to derive from CT
> arrows in the same way.

Yes, right, I can't imagine how I could have forgotten to mention
that, given that I'm a fan of functional programming and Haskell in
particular :-(

Monads are among fundamental things in Haskell; for example, they
allow describing imperative programming in a purely functional way.

> I take that as a sign that CT is in fact more generally useful, but since
> very few people really understand it, it is hard to actually use it.

Yes, I somehow forgot to state that as well :-(

> Something like SymPy supporting CT would help CT.

Yes, and I think I did mention that having CT-related software will be
of great help to people learning CT.

> The remaining question being, as it seems, whether having CT support would
> help SymPy.

Because I haven't managed to find anything CT-related in other
mathematical software, I believe that CT in SymPy will bring SymPy
ahead a bit.  Automating the work with commutative diagrams is of the
same importance as automating symbolic computations: it would make the
life of category theorist a *lot* easier; so, whoever offers this
possibility, will be given many thanks.  The question now reduces to
*how many* people are working with CT.  From what I've heard, CT is
slowly spreading, therefore, I expect that the number of people
interested in it will be increasing, be it slowly.  My judgement may
be biased, though.

Sergiu

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