[Haskell-cafe] Category theory as a design tool

[Arnaud Bailly]

Hello Greg and Alexander,
Thanks for your replies. Funnily, I happen to own the 3 books you mentionned
:-) My interest in category theory is a long standing affair...

Note that owning a book, having read (most of) it and knowing a theory (or
at least its principles and main concepts) is really quite a different thing
from being able to apply it. Although I am certainly able to understand the
Yoneda lemma, I am certainly unable to recognize the opportunity of using
that knowledge to derive some new knowledge about something else. And being
able to define a topoi is very different from being able to construct one or
infer one out of a given category. This is an actual limitation of myself of
course.

Alexander's advice about using diagrams and simple notations is something I
often try to do and something which most of the times end in writing a bunch
of functions and data types in Haskell... What I am really looking for is a
more systematic way of thinking about systems (or system fragments, or
components) in a categorical way, perhaps starting with a bunch of arrows in
some abstract category with objects as components and trying to infer new
objects out of categorical consturctions which are made possible by the
current diagrams (eg. what would be a pullback in such a category ? What
would be its meaning ? Does the question itself have a meaning ?).

Maybe this is really foggy and on the verge to fall into "abstract
nonsense"...

Best regards,
arnaud
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