Monoid in Category of Endofunctors

URI: https://gptkb.org/entity/Monoid_in_Category_of_Endofunctors
GPTKB entity
Statements (36)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:alsoKnownAs Monad (category theory)
gptkbp:application gptkb:Semantics_of_programming_languages
Abstract algebraic structures
Modeling computational effects
gptkbp:category Category of endofunctors on a category C
gptkbp:consistsOf gptkb:Endofunctor
Natural transformations
gptkbp:definedIn Category of endofunctors
gptkbp:example gptkb:Maybe_monad
gptkb:State_monad
List monad
gptkbp:field gptkb:Mathematics
Category theory
gptkbp:formedBy gptkb:Saunders_Mac_Lane
gptkb:Samuel_Eilenberg
gptkbp:generalizes Monoid
gptkbp:hasAxiom Associativity
Unit laws
gptkbp:hasMultiplication Natural transformation (μ: T∘T → T)
gptkbp:hasUnit Identity endofunctor
gptkbp:hasUnitTransformation Natural transformation (η: Id → T)
https://www.w3.org/2000/01/rdf-schema#label Monoid in Category of Endofunctors
gptkbp:introducedIn 1960s
gptkbp:morphismType Natural transformation
gptkbp:operator Composition of endofunctors
gptkbp:relatedConcept gptkb:Functor
Adjunction
Algebra for a monad
Comonad
gptkbp:structureType Monoid
gptkbp:type gptkb:Endofunctor
gptkbp:usedIn gptkb:algebra
Functional programming
gptkbp:bfsParent gptkb:Monads
gptkbp:bfsLayer 6