Ieke Moerdijk (Universiteit Utrecht)

Dendroidal sets

The lectures will provide an introduction to the theory of dendroidal sets. The category of dendroidal sets is an extension of that of simplicial sets, suitable for studying the homotopy theory of operads. It has an interesting closed symmetric monoidal structure, which is closely related to the Boardman–Vogt tensor product of operads. Also, nerves and homotopy coherent nerves of operads can be constructed as dendroidal sets. These satisfy a weak Kan condition, similar to the condition defining quasi-categories, which is satisfied by nerves and homotopy coherent nerves of enriched categories. If time permits, model structures on dendroidal sets and dendroidal spaces will also be discussed.