The finitary monad-Lawvere theory correspondence

John Power – 13 November 2019

Extending work of Garner on base Set, we give a new account, using enriched category theory, of the correspondence, established by Nishizawa--Power, between finitary monads and Lawvere theories over an arbitrary locally finitely presentable category: the passage from a finitary monad to the corresponding Lawvere theory is exhibited as a free completion of an enriched category under a class of absolute colimits. The extension from base Set to an arbitrary locally finitely presentable category requires enrichment over a bicategory, rather than a monoidal category. The talk will focus on the definitions and constructions rather than upon the proof.

(This is joint work with Richard Garner.)