  We give a new account of the correspondence, first established by
Nishizawa--Power, between finitary monads and Lawvere theories over an
arbitrary locally finitely presentable base. Our account explains this
correspondence in terms of enriched category theory: the passage from a
finitary monad to the corresponding Lawvere theory is exhibited as an instance
of free completion of an enriched category under a class of absolute colimits.
This extends work of the first author, who established the result in the
special case of finitary monads and Lawvere theories over the category of sets;
a novel aspect of the generalisation is its use of enrichment over a
bicategory, rather than a monoidal category, in order to capture the
monad--theory correspondence over all locally finitely presentable bases
simultaneously.
