Almost, I think. A functor is a mapping from the arrows, or morphisms,
in a category to arrows in a category. Identity being a perfectly
cromulent functor.
Category theory is like an (over) generalization of set theory. It
doesn't concern itself with pesky details like what elements and
functions are, it starts with those as just properties of a category.
And, as others have indicated, it's the deep relationship between
category theory and type systems that tends to lead programming
language theorists to investigate it. That and the success of monads,
which from a category theory point of view, are fairly trivial.
-SMD
On 7/12/07, Alexis Hazell
On Thursday 12 July 2007 04:40, Andrew Coppin wrote:
I once sat down and tried to read about Category Theory. I got almost nowhere though; I cannot for the life of my figure out how the definition of "category" is actually different from the definition of "set". Or how a "functor" is any different than a "function". Or... actually, none of it made sense.
Iiuc,
"Set" is just one type of category; and the morphisms of the category "Set" are indeed functions. But morphisms in other categories need not be functions; in the category "Rel", for example, the morphisms are not functions but binary relations.
A "functor" is something that maps functions in one category to functions in another category. In other words, functors point from one or more functions in one category to the equivalent functions in another category. Perhaps they could be regarded as 'meta-functions'.
Hope that helps,
Alexis. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe