Malbos, P., Massacrier, T. and Struth, G. (2024) Single-set cubical categories and their formalisation with a proof assistant. Journal of Automated Reasoning, 68 (4). 20. ISSN 0168-7433
Abstract
We introduce a single-set axiomatisation of cubical ω-categories, including connections and inverses. We justify these axioms by establishing a series of equivalences between the category of single-set cubical ω-categories, and their variants with connections and inverses, and the corresponding cubical ω-categories. We also report on the formalisation of cubical ω-categories with the Isabelle/HOL proof assistant, which has been instrumental in developing the single-set axiomatisation.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Authors. Except as otherwise noted, this author-accepted version of a journal article published in Journal of Automated Reasoning is made available via the University of Sheffield Research Publications and Copyright Policy under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ |
Keywords: | Cubical ω-categories; Formalised mathematics; Isabelle/HOL; Higher-dimensional rewriting |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 21 Oct 2024 14:59 |
Last Modified: | 21 Oct 2024 14:59 |
Status: | Published |
Publisher: | Springer Science and Business Media LLC |
Refereed: | Yes |
Identification Number: | 10.1007/s10817-024-09710-9 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:218707 |