Appears in collection : Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteurs

We will start with recognition criteria for equivalences in (infty,n)-categories, introducing and discussing the latter along the way. From there, we will investigate how the notion of equivalence is encoded in strict higher categories, and time permitting discuss the relation of those notions. This is based on joint work (partially in progress) with Martina Rovelli.