Invertible cells in $\ddot{I}‰$-categories

Abstract

We study coinductive invertibility of cells in weak $\ddot{I}‰$-categories. We use the inductive presentation of weak $\ddot{I}‰$-categories via an adjunction with the category of computads, and show that invertible cells are closed under all operations of $\ddot{I}‰$-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.