Collages of string diagrams

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• Document: (arXiv).

Abstract. We introduce collages of string diagrams as a diagrammatic syntax for glueing multiple monoidal categories. Collages of string diagrams are interpreted as pointed bimodular profunctors. As the main examples of this technique, we introduce string diagrams for bimodular categories, string diagrams for functor boxes, and string diagrams for internal diagrams.

Tags: Open diagram, bimodular tambara.

Bimodular profunctors (or the version of Tambara modules apt to Bimodular categories) provide the necessary structure to consider independent pieces of string diagrams. This explains how the syntax for strong monoidal functor boxes works, but also the theory of open internal string diagrams. As a first example, we introduce string diagrams for bimodular categories: we use them for encoding a race condition in bimodular string diagrams.

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@inproceedings{BraithwaiteRoman2023,
  title={Collages of string diagrams},
  author={Braithwaite, Dylan and Rom{\'a}n, Mario},
  series={{EPTCS}},
  booktitle = {Proceedings of the 6rd Annual International Applied Category Theory
               Conference 2020, {ACT} 2023},
  year={2023}
}

See also

• Open Diagrams via Coend Calculus (Román, 2020) uses a first variant of collages to provide string diagrams for pointed profunctors. It justifies how these form “open diagrams”, or “string diagrams of string diagrams”.