The Produoidal Algebra of Process Decomposition

We introduce the normal produoidal category of monoidal contexts over an arbitrary monoidal category. In the same sense that a monoidal morphism represents a process, a monoidal context represents an incomplete process: a piece of a decomposition, possibly containing missing parts. We characterize m...

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Bibliographic Details
Published in:arXiv.org 2023-01
Main Authors: Earnshaw, Matt, Hefford, James, Román, Mario
Format: Article
Language:English
Subjects:
Decomposition
Online Access:Get full text
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Summary:We introduce the normal produoidal category of monoidal contexts over an arbitrary monoidal category. In the same sense that a monoidal morphism represents a process, a monoidal context represents an incomplete process: a piece of a decomposition, possibly containing missing parts. We characterize monoidal contexts in terms of universal properties. In particular, symmetric monoidal contexts coincide with monoidal lenses, endowing them with a novel universal property. We apply this algebraic structure to the analysis of multi-party interaction protocols in arbitrary theories of processes.
ISSN:2331-8422