ω$类别中的可逆单元

arXiv - MATH - Category Theory Pub Date : 2024-06-17 DOI:arxiv-2406.12127

Thibaut Benjamin, Ioannis Markakis

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引用次数: 0

摘要

我们研究弱$\omega$类中单元的共生可逆性。我们利用弱$\omega$类通过与计算子范畴的一个隶属关系的归纳呈现，并证明可逆单元在$\omega$类的所有操作下都是封闭的。此外，我们还给出了一个在 computads 中可逆性的简单判据，以及一个计算可逆性数据（包括逆数据和取消数据）的算法。

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Invertible cells in $ω$-categories

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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arXiv - MATH - Category Theory

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