Work

Monoidal su-categories

Year: 2026

Type: preprint

Abstract: We introduce monoidal su-categories, an abstract categorical notion of single-input higher-order process over a monoidal category. The definition separates a base category C of lower-order processes from a monoidal category V of holes or supermaps and axiomatizes the compatibility needed for partial application to bipartite processes. For a fixed monoidal base C, monoidal su-categories, monoidal su-functors, and monoidal su-natural transformations form a 2-category MonSuCatC. We then show that the category Optic[C] of coend optics is 2-initial in this 2-category, giving an alternative universal-property characterisation of coend optics as the minimal monoidal theory of single-hole contexts.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.15885

Authors: Wilson, Matt, Chiribella, Giulio

Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Université Paris-Saclay, CentraleSupélec, University of Oxford, University of Hong Kong

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: University College London, Engineering and Physical Sciences Research Council

Award: DTP 2224 University College London

OpenAlex ID: W7203699612

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