monoid-extras-0.6: Various extra monoid-related definitions and utilities
Copyright(c) 2013-2015 diagrams-core team (see LICENSE)
LicenseBSD-style (see LICENSE)
Maintainerdiagrams-discuss@googlegroups.com
Safe HaskellSafe-Inferred
LanguageHaskell2010

Data.Monoid.Endomorphism

Description

The monoid of endomorphisms over any Category.

Synopsis

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

Instances

Instances details
Show (k a a) => Show (Endomorphism k a) Source # 
Instance details

Defined in Data.Monoid.Endomorphism

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

(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 #