N_P3Ch12a_HaskEnrich

Markdown of literate Haskell program. Program source: /src/CTNotes/P3Ch12a_HaskEnrich.lhs

A very short note about viewing Haskell in the context of an enriched category.
Book Ref: Part 3 Chapter 12, enhanced categories

 {-# LANGUAGE PolyKinds #-}
 module CTNotes.P3Ch12a_HaskEnrich where
 import Prelude

In a nutshell, enriched categories are based on association C(a,b) of objects a and b in C, C does not need to have any categorical structure, C(a,b) is an object in some monoidal category V, and V is used to provide categorical structure for C.

Repeating definition from Control.Category

 class Category cat where
    id :: cat a a
    (.) :: cat b c -> cat a b -> cat a c

ghci>  :k Category
Category :: (k -> k -> *) -> Constraint

Hask is a monoidal category with (,) as product and () (Unit) as Identity (see N_P3Ch06c_MonoidalCats). I can think of * (Hask) as V and cat a b as C(a,b) (note cat :: k -> k -> *). This way any kind k can be enriched over Hask.

PolyKinds can be viewed as enriching kinds k over Hask!