Higher Theories and Monads

Nicholas Meadows – 30 June 2021

We extend Bourke and Garner's idempotent adjunction between monads and pretheories to the framework of $\infty$-categories, and exploit this to prove many classical theorems about monads in the $\infty$-categorical setting. Amongst other things, we prove that the category of algebras for an accessible monad on a locally presentable $\infty$ category is locally presentable. We also apply the result to construct examples of $\infty$-categorical monads from pretheories.

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