[2209.09509v3] Data Structures for Topologically Sound Higher-Dimensional Diagram Rewriting
Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Category Theory

arXiv:2209.09509v3 (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
View PDF
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)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.CT
< prev   |   next >
new | recent | 2022-09
Change to browse by:
cs
cs.DS
cs.LO
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)