UOR Monoidal Composition

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

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This is a kernel-space namespace in the Define stage of the PRISM pipeline. It provides the immutable algebraic substrate — ring structure, schema vocabulary, and operation algebra.

Learn more: Pipeline Overview

Class hierarchy

Imports

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

Classes

Name	Subclass Of	Disjoint With	Comment
`MonoidalProduct`	`Thing`		A ⊗ B: the sequential composition of two computations. Output of A feeds input of B.
`MonoidalUnit`	`Thing`		The identity computation I: passes input through unchanged. I ⊗ A ≅ A ≅ A ⊗ I.
`MonoidalAssociator`	`Thing`		The witness that (A⊗B)⊗C ≅ A⊗(B⊗C). The associativity isomorphism.

Properties

Name	Kind	Functional	Domain	Range	Comment
`leftOperand`	Object	true	`MonoidalProduct`	`ComputationDatum`	The left operand in the monoidal product A ⊗ B.
`rightOperand`	Object	true	`MonoidalProduct`	`ComputationDatum`	The right operand in the monoidal product A ⊗ B.
`composedResult`	Object	true	`MonoidalProduct`	`Datum`	The result datum of the composed computation A ⊗ B.
`saturationValue`	Datatype	true	`MonoidalProduct`	`decimal`	σ(A⊗B) relationship: saturation of the sequential composition.
`unitWitnessRef`	Object	true	`MonoidalUnit`	`Certificate`	Certificate witnessing I ⊗ A ≅ A ≅ A ⊗ I.
`associatorLeft`	Object	true	`MonoidalAssociator`	`MonoidalProduct`	The left-grouped product (A⊗B)⊗C.
`associatorRight`	Object	true	`MonoidalAssociator`	`MonoidalProduct`	The right-grouped product A⊗(B⊗C).
`associatorWitnessRef`	Object	true	`MonoidalAssociator`	`Certificate`	Certificate witnessing the associativity isomorphism (A⊗B)⊗C ≅ A⊗(B⊗C).