Postnikov Systems for Higher Categories

The Postnikov tower is one of the earliest tools used to investigate the homotopy types of spaces: it allows one to reconstruct a space from Eilenberg–Maclane spaces and hence to study its homotopical properties in terms of cohomology. In this talk, I will describe a version of the Postnikov tower for (oo, n)-categories, inspired by ideas of Lurie. This will follow from a general analysis of Postnikov-type systems in oo-categories, including the ``k-invariants'' that classify them. For example, given a functorial choice of such a system for the objects of a monoidal category V, one often obtains induced Postnikov systems for algebras in V and for V-enriched categories. Based on joint work with Yonatan Harpaz and Matan Prasma.