On the monadicity of finitary monads Original Research Article

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