25 Dec
2010
25 Dec
'10
12:29 a.m.
On 12/24/10 12:26 AM, C. McCann wrote:
As far as I understand (which may not actually be all that far), contravariant functors just go to or from an opposite category, a distinction that is purely a matter of definition, not anything intrinsic.
Yes.
On the other hand, Applicative and Monad are based on endofunctors specifically, i.e. functors from a category to itself, which would seem to necessarily exclude functors from a category to its opposite.
Except for when the category is self-dual (i.e., C = C^op). But self-duality brings all sorts of other fun things into play as well. -- Live well, ~wren