[2209.09509] Data Structures for Topologically Sound Higher-Dimensional Diagram Rewriting
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Mathematics > Category Theory

arXiv:2209.09509 (math)
[Submitted on 20 Sep 2022 (v1), last revised 31 Jul 2023 (this version, v3)]

Title:Data Structures for Topologically Sound Higher-Dimensional Diagram Rewriting

Authors:Amar Hadzihasanovic, Diana Kessler
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Abstract:We present a computational implementation of diagrammatic sets, a model of higher-dimensional diagram rewriting that is "topologically sound": diagrams admit a functorial interpretation as homotopies in cell complexes. This has potential applications both in the formalisation of higher algebra and category theory and in computational algebraic topology. We describe data structures for well-formed shapes of diagrams of arbitrary dimensions and provide a solution to their isomorphism problem in time O(n^3 log n). On top of this, we define a type theory for rewriting in diagrammatic sets and provide a semantic characterisation of its syntactic category. All data structures and algorithms are implemented in the Python library rewalt, which also supports various visualisations of diagrams.
Comments: In Proceedings ACT 2022, arXiv:2307.15519
Subjects: Category Theory (math.CT); Data Structures and Algorithms (cs.DS); Logic in Computer Science (cs.LO)
Cite as: arXiv:2209.09509 [math.CT]
  (or arXiv:2209.09509v3 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.2209.09509
Journal reference: EPTCS 380, 2023, pp. 111-127
Related DOI: https://doi.org/10.4204/EPTCS.380.7

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Tue, 20 Sep 2022 06:54:24 UTC (42 KB)
[v2] Thu, 29 Sep 2022 09:03:42 UTC (41 KB)
[v3] Mon, 31 Jul 2023 10:29:58 UTC (34 KB)
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