On the monadicity of finitary monads

Abstract

In 1993, Kelly and Power showed that the category of finitary monads on a locally finitely presentable category A is of descent type over a power of A ; here we establish the stronger result that the forgetful functor in question is monadic. Both their result and ours remain true in the V -enriched case for suitable monoidal categories V . Generalizing further, we obtain a monadicity result for algebras for an operad.