Weakly invertible cells in a weak $\ddot{I}‰$-category

Abstract

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

21 pages. Published version. Comments welcome!