Mathematics > Category Theory
[Submitted on 27 Mar 2023 (v1), last revised 20 Nov 2024 (this version, v3)]
Title:Weakly invertible cells in a weak $ω$-category
View PDF HTML (experimental)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.
Submission history
From: Yuki Maehara [view email][v1] Mon, 27 Mar 2023 03:47:44 UTC (29 KB)
[v2] Tue, 16 Jan 2024 02:13:03 UTC (37 KB)
[v3] Wed, 20 Nov 2024 23:16:11 UTC (37 KB)
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