Statements (116)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
gptkb:programming_language |
| gptkbp:alternativeName |
Monad
functor monad |
| gptkbp:definedIn |
gptkb:Mathematics
|
| gptkbp:example |
gptkb:Contravariant_functor
gptkb:Covariant_functor gptkb:Endofunctor gptkb:Forgetful_functor gptkb:Hom_functor gptkb:IO_monad gptkb:Maybe_monad gptkb:State_monad List monad Reader monad Writer monad |
| gptkbp:field |
Category theory
|
| gptkbp:formedBy |
gptkb:Mathematics
Computer science Category theory |
| gptkbp:generalizes |
gptkb:Homomorphism
|
| gptkbp:hasComponent |
gptkb:Functor
Natural transformation |
| gptkbp:hasType |
gptkb:Adjoint_functor
gptkb:Bifunctor gptkb:Co-functor gptkb:Endofunctor gptkb:Faithful_functor gptkb:Forgetful_functor gptkb:Lax_functor gptkb:Monoidal_functor gptkb:Op-functor gptkb:Pseudo-functor gptkb:Representable_functor gptkb:Symmetric_monoidal_functor Additive functor Functoriality Contravariant Covariant Coend functor Colax functor Colimit functor Corepresentable functor Equivalence of categories Essentially surjective functor Exact functor Full and faithful functor Full functor Functor category Functorial adjunction Functorial category Functorial cokernel Functorial colimit Functorial construction Functorial corestriction Functorial coretraction Functorial equivalence Functorial extension Functorial functor Functorial image Functorial isomorphism Functorial kernel Functorial limit Functorial mapping Functorial morphism Functorial object Functorial preimage Functorial property Functorial quotient Functorial restriction Functorial retraction Functorial section Functorial structure Functorial subobject Functorial transformation Lax monoidal functor Limit functor Non-split functor Pointed functor Pre-functor Split functor Strict functor Strong functor Unpointed functor Weak functor |
| https://www.w3.org/2000/01/rdf-schema#label |
Functor
|
| gptkbp:introduced |
gptkb:Saunders_Mac_Lane
|
| gptkbp:introducedIn |
1960s
|
| gptkbp:legalSystem |
Associativity
Left identity Right identity |
| gptkbp:mapType |
Category C to category D
Objects and morphisms between categories |
| gptkbp:notation |
F: C → D
|
| gptkbp:operator |
return
bind |
| gptkbp:preserves |
Composition of morphisms
Identity morphisms Structure of categories |
| gptkbp:relatedTo |
gptkb:Monads
Categories Monoid Natural transformation Applicative functor Kleisli category |
| gptkbp:usedFor |
Handling side effects
Sequencing computations |
| gptkbp:usedIn |
gptkb:algebra
gptkb:Topology gptkb:Haskell Computer science Category theory Functional programming |
| gptkbp:bfsParent |
gptkb:Monadology
|
| gptkbp:bfsLayer |
4
|