homotopy.io: A Proof Assistant for Finitely-Presented Globular n-Categories

Authors Nathan Corbyn , Lukas Heidemann , Nick Hu , Chiara Sarti , Calin Tataru , Jamie Vicary



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Author Details

Nathan Corbyn
  • University of Oxford, Oxford, UK
Lukas Heidemann
  • University of Oxford, Oxford, UK
Nick Hu
  • University of Oxford, Oxford, UK
Chiara Sarti
  • University of Cambridge, Cambridge, UK
Calin Tataru
  • University of Cambridge, Cambridge, UK
Jamie Vicary
  • University of Cambridge, Cambridge, UK

Acknowledgements

The authors would like to thank Anastasia Courtney, Yulong Huang, and Jasper Parish for their contributions during their summer internships, Akvilė Valentukonytė and Klaudia Urbanska for their contributions during their undergraduate projects, and Manuel Araújo, Wilf Offord, and Hao Xu for extensive testing of the tool and valuable feedback. We are also grateful to the students of the "Categorical Quantum Mechanics" course at Oxford, and the "Advanced Topics in Category Theory" course at Cambridge for testing and feedback.

Cite AsGet BibTex

Nathan Corbyn, Lukas Heidemann, Nick Hu, Chiara Sarti, Calin Tataru, and Jamie Vicary. homotopy.io: A Proof Assistant for Finitely-Presented Globular n-Categories. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 30:1-30:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.FSCD.2024.30

Abstract

We present the proof assistant homotopy.io for working with finitely-presented semistrict higher categories. The tool runs in the browser with a point-and-click interface, allowing direct manipulation of proof objects via a graphical representation. We describe the user interface and explain how the tool can be used in practice. We also describe the essential subsystems of the tool, including collapse, contraction, expansion, typechecking, and layout, as well as key implementation details including data structure encoding, memoisation, and rendering. These technical innovations have been essential for achieving good performance in a resource-constrained setting.

Subject Classification

ACM Subject Classification
  • Software and its engineering → Software notations and tools
Keywords
  • Higher category theory
  • proof assistant
  • string diagrams

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