UOR Monoidal Composition

IRI
https://uor.foundation/monoidal/
Prefix
monoidal:
Space
kernel
Comment
Sequential composition of computations via monoidal product A ⊗ B.

Imports

  • https://uor.foundation/op/
  • https://uor.foundation/reduction/
  • https://uor.foundation/cert/
  • https://uor.foundation/morphism/
  • https://uor.foundation/schema/

Classes

NameIRISubclass OfDisjoint WithComment
MonoidalProducthttps://uor.foundation/monoidal/MonoidalProducthttp://www.w3.org/2002/07/owl#ThingA ⊗ B: the sequential composition of two computations. Output of A feeds input of B.
MonoidalUnithttps://uor.foundation/monoidal/MonoidalUnithttp://www.w3.org/2002/07/owl#ThingThe identity computation I: passes input through unchanged. I ⊗ A ≅ A ≅ A ⊗ I.
MonoidalAssociatorhttps://uor.foundation/monoidal/MonoidalAssociatorhttp://www.w3.org/2002/07/owl#ThingThe witness that (A⊗B)⊗C ≅ A⊗(B⊗C). The associativity isomorphism.

Properties

NameKindFunctionalDomainRangeComment
leftOperandObjecttruehttps://uor.foundation/monoidal/MonoidalProducthttps://uor.foundation/morphism/ComputationDatumThe left operand in the monoidal product A ⊗ B.
rightOperandObjecttruehttps://uor.foundation/monoidal/MonoidalProducthttps://uor.foundation/morphism/ComputationDatumThe right operand in the monoidal product A ⊗ B.
composedResultObjecttruehttps://uor.foundation/monoidal/MonoidalProducthttps://uor.foundation/schema/DatumThe result datum of the composed computation A ⊗ B.
saturationValueDatatypetruehttps://uor.foundation/monoidal/MonoidalProducthttp://www.w3.org/2001/XMLSchema#decimalσ(A⊗B) relationship: saturation of the sequential composition.
unitWitnessRefObjecttruehttps://uor.foundation/monoidal/MonoidalUnithttps://uor.foundation/cert/CertificateCertificate witnessing I ⊗ A ≅ A ≅ A ⊗ I.
associatorLeftObjecttruehttps://uor.foundation/monoidal/MonoidalAssociatorhttps://uor.foundation/monoidal/MonoidalProductThe left-grouped product (A⊗B)⊗C.
associatorRightObjecttruehttps://uor.foundation/monoidal/MonoidalAssociatorhttps://uor.foundation/monoidal/MonoidalProductThe right-grouped product A⊗(B⊗C).
associatorWitnessRefObjecttruehttps://uor.foundation/monoidal/MonoidalAssociatorhttps://uor.foundation/cert/CertificateCertificate witnessing the associativity isomorphism (A⊗B)⊗C ≅ A⊗(B⊗C).