An enriched view on the extended finitary monad-Lawvere theory correspondence

Anthony Power, Richard Garner

Research output: Contribution to journalArticle

Abstract

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.
Original languageEnglish
Pages (from-to)1--23
Number of pages14
JournalLogical Methods in Computer Science
StateAccepted/In press - 1 Jan 2018

Fingerprint

Monads
Correspondence
Enriched category
Bicategory
Colimit
Category theory
Monoidal category
Completion
Arbitrary

Keywords

  • bicategory, enriched category, monad, Lawvere theory

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

An enriched view on the extended finitary monad-Lawvere theory correspondence. / Power, Anthony; Garner, Richard.

In: Logical Methods in Computer Science, 01.01.2018, p. 1--23.

Research output: Contribution to journalArticle

Power, Anthony; Garner, Richard / An enriched view on the extended finitary monad-Lawvere theory correspondence.

In: Logical Methods in Computer Science, 01.01.2018, p. 1--23.

Research output: Contribution to journalArticle

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