Implement internal hom objects for Day? about kan-extensions HOT 6 CLOSED

Actually, it seems this is just CoT in disguise. Perhaps it would be better to just write the evaluation and composition functions for CoT instead:

eval :: Day (CoT w m) w a -> m a
compose :: Day (CoT g h) (CoT f g) a -> CoT f h a

from kan-extensions.

Interestingly it was this thing that made me start thinking about Day in the first place.

from kan-extensions.

(That and Gershom bugging me to figure out what Day convolution would mean in Haskell)

from kan-extensions.

Actually, I got this wrong, they're not quite the same.CoT w m has an extra m inside the w on the left:

newtype CoT w m a = CoT { runCoT :: forall r. w (a -> m r) -> m r }

newtype Hom w m a = CoT { runCoT :: forall r. w (a -> r) -> m r }

and CoT w m is a Monad for any Comonad w, whereas Monad (Hom w m) also needs Monad m.

from kan-extensions.

Yep. I made a similar mistake connecting Day with Rift.

from kan-extensions.

there it fails to be an isomorphism without a something being a left adjoint.

from kan-extensions.