Algebra.Category

Documentation

class Category (cat :: k -> k -> Type) where

A class for categories. Instances should satisfy the laws

f . id  =  f  -- (right identity)
id . f  =  f  -- (left identity)
f . (g . h)  =  (f . g) . h  -- (associativity)

Associated Types

type Con (a :: k) :: Constraint

Methods

(.) :: (Con a, Con b, Con c) => (b `cat` c) -> (a `cat` b) -> a `cat` c infixr 9

id :: Con a => a `cat` a

Instances

Category ((->) :: Type -> Type -> Type)

Defined in Algebra.Category

Associated Types

type Con a :: Constraint

Methods

(.) :: (Con a, Con b, Con c) => (b -> c) -> (a -> b) -> a -> c

id :: Con a => a -> a

Ring s => Category (Mat s :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in Algebra.Linear

Associated Types

type Con a :: Constraint

Methods

(.) :: (Con a, Con b, Con c) => Mat s b c -> Mat s a b -> Mat s a c

id :: Con a => Mat s a a