We extend Bourke and Garner’s idempotent adjunction between monads and pretheories to the framework of ∞-categories, and exploit this to prove many classical theorems about monads in the ∞-categorical setting. Among other things, we prove that the category of algebras for an accessible monad on a locally presentable ∞ category is locally presentable. We also apply the result to construct examples of ∞-categorical monads from pretheories.
This video is part of Masaryk University‘s Algebra seminar.
Related videos in this area: Algebraic topology, Category theory, Higher category theory, Homotopy theory, Logic, Monads, Topology
