On the construction of action monads as an adjoint functor from monoids to strong monads (all in the generality of enriched category theory):
Given a symmetric closed monoidal category $V$, a $V$-enriched category $A$ with underlying ordinary category $A_0$ and a subcategory $\Sigma$ of $A_0$ containing the identities of $A_0$, H. Wolff defines the corresponding theory of a localization of an enriched category:
H. Wolff, $V$-localizations and $V$-triples, Dissertation, University of Illinois-Urbana, 1970.
H. Wolff, $V$-localizations and $V$-monads, J. Alg. 24, 405-438, 1973, MR310041, doi;
H. Wolff, V-localizations and $V$-monads. II, Pacific J. Math. 63 (1976), no. 2, 579–589, MR412253, euclid;
H. Wolff, $V$-localizations and $V$-Kleisli algebras, Manuscripta Math. 16 (1975), no. 3, 203–228, MR382383, doi
On free monads:
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