Richard Garner ; John Power - 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 - https://doi.org/10.23638/LMCS-14(1:16)2018
An enriched view on the extended finitary monad--Lawvere theory correspondenceArticle

Authors: Richard Garner ; John Power

    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.


    Volume: Volume 14, Issue 1
    Published on: February 27, 2018
    Accepted on: January 11, 2018
    Submitted on: August 1, 2017
    Keywords: Mathematics - Category Theory,18C10, 18C35, 18D20
    Funding:
      Source : OpenAIRE Graph
    • Discovery Projects - Grant ID: DP160101519; Funder: Australian Research Council (ARC); Code: DP160101519
    • ARC Future Fellowships - Grant ID: FT160100393; Funder: Australian Research Council (ARC); Code: FT160100393

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