Apparaît dans la collection : 2023 - T2 - WS3 - Dg-manifolds in geometry and physics

The dendroidal formalism offers a powerful approach to defining operads as specific presheaves on a tree-based category. This combinatorial framework enables the definition of ∞-operads, wherein composition is determined up to homotopy via presheaves that satisfy a weak dendroidal inner Kan condition. Notably, the homotopy theory of ∞-operads has been shown to be equivalent, in both Quillen's sense and Lurie's ∞-categorical sense, to the theories of topological and simplicial operads.

In this talk we will review these concepts and present some open questions in enriched settings.