Infinity Categories

The aim of this reading group is to study the basics of ∞-categories, following Lurie’s treatment in [Lur09] and the Kerodon project [Lur]. ∞-categories (and particularly (∞, 1)−categories) are quickly becoming an indispensable tool in many areas of mathematics, notably in homotopy theory, (derived) algebraic geometry [Lur04] and mathematical physics (under the guise of TQFTs [Lur08]). In this reading group, we aim to understand the basic definitions and constructions in order to be able to engage with literature using the language of ∞-categories, and to see some explicit applications, such as the theory of stable ∞-categories (and their relationship to derived categories) and the cobordism hypothesis.

Organizer: Tudor-Ioan Caba