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arXiv · 2401.10553

Single-set cubical categories and their formalisation with a proof assistant (extended version)

Philippe Malbos·Tanguy Massacrier·Georg Struth
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Abstract

We introduce a single-set axiomatisation of cubical $\omega$-categories, including connections and inverses. We justify these axioms by establishing a series of equivalences between the category of single-set cubical $\omega$-categories, and their variants with connections and inverses, and the corresponding cubical $\omega$-categories. We also report on the formalisation of cubical $\omega$-categories with the Isabelle/HOL proof assistant, which has been instrumental in developing the single-set axiomatisation.

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Philippe Malbos, Tanguy Massacrier, Georg Struth. 2024-01-19. Single-set cubical categories and their formalisation with a proof assistant (extended version). https://arxiv.org/abs/2401.10553

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