Higher theories and monads

We extend Bourke and Garner's idempotent adjunction between monads and pretheories to the framework of -categories and we use this to prove many classical results about monads in the -categorical framework. Amongst other things, we show that the category of algebras for an accessible monads on a locally presentable -category E is again locally presentable, and that a diagram of accessible monads on a locally presentable -category admits a colimit. Our results also provide a new and simpler way to construct and describe monads in terms of theories.