We characterize a universal 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. In particular, symmetric monoidal contexts coincide with monoidal lenses and endow them with a novel universal property. We apply this algebraic structure to the analysis of multi-party protocols in arbitrary theories of processes.
@InProceedings{earnshaw_et_al:LIPIcs.CSL.2024.25, author = {Earnshaw, Matt and Hefford, James and Rom\'{a}n, Mario}, title = {{The Produoidal Algebra of Process Decomposition}}, booktitle = {32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)}, pages = {25:1--25:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-310-2}, ISSN = {1868-8969}, year = {2024}, volume = {288}, editor = {Murano, Aniello and Silva, Alexandra}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.25}, URN = {urn:nbn:de:0030-drops-196688}, doi = {10.4230/LIPIcs.CSL.2024.25}, annote = {Keywords: monoidal categories, profunctors, lenses, duoidal categories} }
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