On the monadicity of finitary monads


Stephen Lack


Research Report 97-29
To appear in Journal of Pure and Applied Algebra
Date: 21 October 1997


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.

Key phrases

monad. locally presentable category. operad.

AMS Subject Classification (1991)

Primary: 18C15
Secondary: 18C20, 18D20


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