On the monadicity of finitary monads

Steve Lack – 30 April 1997

In Kelly and Power, Adjunctions whose Counits are Coequalizers, and Presentations of Finitary Enriched Monads, JPAA (1993) it was shown that finitary monads on a locally finitely presentable category A were of descent type over a power of A; here we show that the forgetful functor in question is in fact monadic. Both their result and ours remain true in the V-enriched case for suitable monoidal categories V. (Note added 15/01/98) This work now exists as a preprint On the monadicity of finitary monads, and will appear in the Journal of Pure and Applied Algebra.