Hi Café.
I'm wracking my brain trying to figure out a simple, reasonably general, implementation for a category instance for pairs of categories.
So far I've looked at [1], which seems great, but doesn't use the built-in category instance, and [2], which I'm just not sure about.
Ideally I'd like to be able to express something like -
instance (Category a, Category b) => Category (Product a b) where
id = Product id id
Product o1 o2 . Product i1 i2 = Product (o1 . i1) (o2 . i2)
However, it all falls apart when I actually try to define anything. Is this possible? If not, why not?
As far as I can tell the issue boils down to not being able to translate "Category i o" to "Product (Fst i) (Fst o) (Snd i) (Snd o)" without breaking the kind expectation of the category instance.
Please help me, I'm having a bad brain day :-)