Safe Haskell	Safe
Language	Haskell2010

Algebra.Category

Synopsis

class Category (cat :: k -> k -> Type) where
- type Con (a :: k) :: Constraint
- (.) :: (Con a, Con b, Con c) => (b `cat` c) -> (a `cat` b) -> a `cat` c
- id :: Con a => a `cat` a

Documentation

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

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

Methods

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

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

Instances

Category ((->) :: Type -> Type -> Type) Source #
Instance details Defined in Algebra.Category Associated Types type Con a :: Constraint Source # Methods (.) :: (Con a, Con b, Con c) => (b -> c) -> (a -> b) -> a -> c Source # id :: Con a => a -> a Source #
Ring s => Category (Mat s :: (Type -> Type) -> (Type -> Type) -> Type) Source #
Instance details Defined in Algebra.Linear Associated Types type Con a :: Constraint Source # Methods (.) :: (Con a, Con b, Con c) => Mat s b c -> Mat s a b -> Mat s a c Source # id :: Con a => Mat s a a Source #