Garner, Richard and Power, John - An enriched view on the extended finitary monad--Lawvere theory correspondence

lmcs:3828 - Logical Methods in Computer Science, February 27, 2018, Volume 14, Issue 1
An enriched view on the extended finitary monad--Lawvere theory correspondence

Authors: Garner, Richard and Power, John

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.


Source : oai:arXiv.org:1707.08694
DOI : 10.23638/LMCS-14(1:16)2018
Volume: Volume 14, Issue 1
Published on: February 27, 2018
Submitted on: August 1, 2017
Keywords: Mathematics - Category Theory,18C10, 18C35, 18D20


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