Chiara Sava

Finite dimensional algebras can be understood by studying quivers, which are sets of vertices together with sets of arrows connecting them. We can associate a quiver to the module category of an algebra as well as to its derived category. Even when we pass to a more general setting, such as derivators, which are an enhancement of the derived category, by looking at a suitable quiver, we will be able to see where representation theory meets homotopy theory. In particular, we will explain the fundamental equivalence given by the infinity-Dold Kan correspondence.