monoids-0.1.36: Monoids, specialized containers and a general map/reduce framework Source code Contents Index

Data.Monoid.Categorical Portability portable Stability experimental Maintainer ekmett@gmail.com

Contents Generalized Endo Monoids as Categories

Description

Synopsis

module Data.Monoid.Reducer module Control.Category data GEndo k a = GEndo { getGEndo :: k a a } data CMonoid m n o categoryToMonoid :: CMonoid m m m -> m monoidToCategory :: Monoid m => m -> CMonoid m m m

Documentation

module Data.Monoid.Reducer

module Control.Category

Generalized Endo

data GEndo k a Source

The Monoid of the endomorphisms over some object in an arbitrary Category. Constructors GEndo getGEndo :: k a a Instances Category k => RightModule Natural (GEndo k a) Category k => LeftModule Natural (GEndo k a) Category k => Module Natural (GEndo k a) Category k => Monoid (GEndo k a)

Monoids as Categories

data CMonoid m n o Source

A Monoid is just a Category with one object. This fakes that with a GADT Instances Reducer c m => Reducer c (CMonoid m m m) Monoid m => RightModule Natural (CMonoid m m m) Monoid m => LeftModule Natural (CMonoid m m m) Monoid m => Module Natural (CMonoid m m m) Monoid m => Category (CMonoid m) Monoid m => Monoid (CMonoid m m m) Monoid m => Reducer (CMonoid m m m) m

categoryToMonoid :: CMonoid m m m -> m Source

Extract the Monoid from its representation as a Category

monoidToCategory :: Monoid m => m -> CMonoid m m m Source

Convert a value in a Monoid into an arrow in a Category.

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