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arXiv · 2303.14907

Weakly invertible cells in a weak $\omega$-category

Soichiro Fujii·Keisuke Hoshino·Yuki Maehara
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Abstract

We study weakly invertible cells in weak $\omega$-categories in the sense of Batanin-Leinster, adopting the coinductive definition of weak invertibility. We show that weakly invertible cells in a weak $\omega$-category are closed under globular pasting. Using this, we generalise elementary properties of weakly invertible cells known to hold in strict $\omega$-categories to weak $\omega$-categories, and show that every weak $\omega$-category has a largest weak $\omega$-subgroupoid.

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Soichiro Fujii, Keisuke Hoshino, Yuki Maehara. 2023-03-27. Weakly invertible cells in a weak $\omega$-category. https://doi.org/10.21136/hs.2024.14

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