Séminaire Algèbre Géométrie Algébrique Topologie Algébrique
jeudi 12 mars 2020 à 11:30 - salle 430
Joachim Kock (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.