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. Amongst 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 is joint work with S. Henry (UOttawa).