Francesca Pratali: Localization of infinity-operads

The theory of $\infty$-operads describes higher algebraic structures in
$\infty$-categories and is closely related to symmetric monoidal
$\infty$-categories. In homotopical settings, $\infty$-operads often
arise through localization, the process of freely inverting a class of
morphisms.

Localization is well understood at the level of $\infty$-categories:
Joyal’s delocalization theorem asserts that every $\infty$-category is
weakly equivalent to the localization of a discrete category, while the
classical work of Barwick and Kan shows that this process establishes an
equivalence at the level of homotopy theories.

In this talk, I will present a delocalization theorem for
$\infty$-operads, showing that every $\infty$-operad is weakly
equivalent to the localization of a discrete operad. I will sketch the
combinatorial approach, based on the dendroidal formalism, and I will
also mention applications to the homotopy theory of $\infty$-operads,
including a generalization of the Barwick–Kan theorem in joint work with
Arakawa and Carmona.