Talk 4: Stable ∞-categories
Nils Witt (Universität Heidelberg)

References: [3], [7]
The goal of this talk is to explain [3, §1.1, §1.2]. Define stable ∞-categories [3, Definition 1.1.1.9.] and show (without going into to much detail) that the homotopy category of an ∞-category is triangulated [3, Theorem 1.1.2.14.] (for example, one could prove that it is additive and explain how distinguished triangles in the homotopy category are defined). State [3, 1.1.3.1 – 1.1.3.4]. Go then on to [3, §1.2.1] and introduce t-structures on stable ∞-categories. One could also take a look into [7, §5] for an overview.