Séminaire Algèbre Géométrie Algébrique Topologie Algébrique :

Le 12 mars 2020 à 11:30 - salle 430

Présentée par Kock Joachim - Universitat Autònoma de Barcelona

Infinity operads as polynomial monads

In the first half I will explain the notions of operads, monads, species, and polynomial functors, and say a bit about the role of polynomial functors in representation theory, universal algebra, logic, and computer science. The main message in this part, meant to be quite elementary, is that polynomial monads are not general enough to capture operads, although this would have been a nice result.
In the second half I will pass to the infinity world. Remarkably, here the problems go away, and leads to certain polynomial monads being a model for infinity-operads. The main theorem states an equivalence of infinity-categories with the dendroidal Segal spaces of Cisinski and Moerdijk, one of the known equivalent models for infinity-operads. This is joint work with David Gepner and Rune Haugseng.