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arXiv · 2406.12127

Invertible cells in $\omega$-categories

Thibaut Benjamin·Ioannis Markakis
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Abstract

We study coinductive invertibility of cells in weak $\omega$-categories. We use the inductive presentation of weak $\omega$-categories via an adjunction with the category of computads, and show that invertible cells are closed under all operations of $\omega$-categories. Moreover, we give a simple criterion for invertibility in computads, together with an algorithm computing the data witnessing the invertibility, including the inverse, and the cancellation data.

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Thibaut Benjamin, Ioannis Markakis. 2024-06-17. Invertible cells in $\omega$-categories. https://arxiv.org/abs/2406.12127

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