Data.Category

Contents

Description

Synopsis

Category

class Category (~>) whereSource

An instance of Category (~>) declares the arrow (~>) as a category.

Associated Types

data Obj (~>) :: * -> *Source

Methods

src :: (a ~> b) -> Obj ~> aSource

tgt :: (a ~> b) -> Obj ~> bSource

id :: Obj ~> a -> a ~> aSource

(.) :: (b ~> c) -> (a ~> b) -> a ~> cSource

Instances

Category (->)	The category with Haskell types as objects and Haskell functions as arrows.
Category Cat	`Cat` is the category with categories as objects and funtors as arrows.
Category Void
Category Pair
Category Unit
Category AdjArrow
Category Boolean	`Boolean` is the category with true and false as objects, and an arrow from false to true.
Category Omega
Category ~> => Category (Op ~>)	`Op (~>)` is opposite category of the category `(~>)`.
Category (Discrete n) => Category (Discrete (S n))
Category (Discrete Z)
Monoid m => Category (MonoidA m)
Category ~> => Category (Peano ~>)
(Category c, Category d) => Category (Nat c d)	Functor category D^C. Objects of D^C are functors from C to D. Arrows of D^C are natural transformations.
(Category c1, Category c2) => Category (:*: c1 c2)	The product category of category `c1` and `c2`.
(Dom m ~ ~>, Cod m ~ ~>, Category ~>, Monad m) => Category (Kleisli ~> m)
Category (Dialg f g)
(Category (Dom t), Category (Dom s)) => Category (:/\: t s)

Opposite category

data Op whereSource

Constructors

Op :: (a ~> b) -> Op ~> b a

Instances

Op (~>) is opposite category of the category (~>).