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

Anthony Power, Richard Garner

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2 Citations (SciVal)
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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
Article number16
Pages (from-to)1-23
Number of pages14
JournalLogical Methods in Computer Science
Issue number1
Publication statusPublished - 27 Feb 2018


  • bicategory, enriched category, monad, Lawvere theory
  • Finitary monad
  • Enrichment in a bicategory
  • Locally finitely presentable category
  • Lawvere theory
  • Absolute colimits

ASJC Scopus subject areas

  • Mathematics(all)
  • Theoretical Computer Science
  • Computer Science(all)


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