**abstract:**
Operads are combinatorial objects arisen in algebraic topology to model the up-to-homotopy associative algebra structure of loop spaces. Operads can be thought of as
sequences of **spaces**, whose points are n-inputs 1-output operations, together with composition laws between them. When we consider these relations only up to homotopy
of maps of topological spaces, we talk about oo-operads.
In this talk, we explain how oo-operads can be modeled as **dendroidal sets**, namely functors from a category of trees to sets. We will show how, given any dendroidal set X,
we can functorially construct a strict operad \Omega*X admitting a map into X. We call this the 'root functor', and prove that it induces a weak operadic equivalence between X
and the localization of \Omega*X at some set of morphisms.
In a nutshell, we prove that any oo-operad is the localization of a strict operad!

Tue 1 Oct, 16:00 - 16:35, Aula Dini

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