Operads, trees and the root functor
speaker: Francesca (CONTRIBUTED TALK) Prataliabstract: 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 \OmegaX 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 \OmegaX at some set of morphisms. In a nutshell, we prove that any oo-operad is the localization of a strict operad!
timetable:
Tue 1 Oct, 16:00 - 16:35, Aula Dini
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