Copyright	(c) 2013-2015 diagrams-core team (see LICENSE)
License	BSD-style (see LICENSE)
Maintainer	diagrams-discuss@googlegroups.com
Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Monoid.Endomorphism

Description

The monoid of endomorphisms over any Category.

Synopsis

newtype Endomorphism k a = Endomorphism {
- getEndomorphism :: k a a
}

Documentation

newtype Endomorphism k a Source #

An Endomorphism in a given Category is a morphism from some object to itself. The set of endomorphisms for a particular object form a monoid, with composition as the combining operation and the identity morphism as the identity element.

Constructors

Endomorphism
Fields getEndomorphism :: k a a

Instances

Instances details

Show (k a a) => Show (Endomorphism k a) Source #
Instance details Defined in Data.Monoid.Endomorphism Methods showsPrec :: Int -> Endomorphism k a -> ShowS # show :: Endomorphism k a -> String # showList :: [Endomorphism k a] -> ShowS #
Semigroupoid k => Semigroup (Endomorphism k a) Source #
Instance details Defined in Data.Monoid.Endomorphism Methods (<>) :: Endomorphism k a -> Endomorphism k a -> Endomorphism k a # sconcat :: NonEmpty (Endomorphism k a) -> Endomorphism k a # stimes :: Integral b => b -> Endomorphism k a -> Endomorphism k a #
(Semigroupoid k, Category k) => Monoid (Endomorphism k a) Source #
Instance details Defined in Data.Monoid.Endomorphism Methods mempty :: Endomorphism k a # mappend :: Endomorphism k a -> Endomorphism k a -> Endomorphism k a # mconcat :: [Endomorphism k a] -> Endomorphism k a #
(Category k, Groupoid k) => Group (Endomorphism k a) Source #
Instance details Defined in Data.Monoid.Endomorphism Methods invert :: Endomorphism k a -> Endomorphism k a # (~~) :: Endomorphism k a -> Endomorphism k a -> Endomorphism k a # pow :: Integral x => Endomorphism k a -> x -> Endomorphism k a #