[2210.08914] A Category of Surface-Embedded Graphs
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Computer Science > Logic in Computer Science

arXiv:2210.08914 (cs)
[Submitted on 17 Oct 2022 (v1), last revised 31 Jul 2023 (this version, v2)]

Title:A Category of Surface-Embedded Graphs

Authors:Malin Altenmüller, Ross Duncan
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Abstract:We introduce a categorical formalism for rewriting surface-embedded graphs. Such graphs can represent string diagrams in a non-symmetric setting where we guarantee that the wires do not intersect each other. The main technical novelty is a new formulation of double pushout rewriting on graphs which explicitly records the boundary of the rewrite. Using this boundary structure we can augment these graphs with a rotation system, allowing the surface topology to be incorporated.
Comments: In Proceedings ACT 2022, arXiv:2307.15519
Subjects: Logic in Computer Science (cs.LO)
Cite as: arXiv:2210.08914 [cs.LO]
  (or arXiv:2210.08914v2 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2210.08914
Journal reference: EPTCS 380, 2023, pp. 41-62
Related DOI: https://doi.org/10.4204/EPTCS.380.3

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Mon, 17 Oct 2022 10:11:09 UTC (5,016 KB)
[v2] Mon, 31 Jul 2023 10:27:33 UTC (1,694 KB)
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