Algebras over ∞-operads

Abstract

Operads are an efficient tool to study algebraic structures in homotopy theory. In recent years homotopy-theoretic methods have been infused into other areas of mathematics, most notably algebraic geometry, through the use of higher category theory and in particular infinity-categories. In order to accomodate the use of operads in this setting, a theory of infinity-operads has been introduced by Moerdijk and Weiss several years ago through the use of so-called dendroidal sets. This thesis introduces a new notion of algebra over an infinity-operad which is completely intrinsic to the formalism of dendroidal sets and provides a flexible framework to work with these algebras. Our inspiration comes from the classical Grothendieck construction and Lurie's generalization of it to the setting of infinity-categories.