Australian Category Seminar

On the monadicity of finitary monads

Steve Lackยท30 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.

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