Notions of Lawvere theory

Stephen Lack*, Jiří Rosický

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


Categorical universal algebra can be developed either using Lawvere theories (single-sorted finite product theories) or using monads, and the category of Lawvere theories is equivalent to the category of finitary monads on Set. We show how this equivalence, and the basic results of universal algebra, can be generalized in three ways: replacing Set by another category, working in an enriched setting, and by working with another class of limits than finite products.

Original languageEnglish
Pages (from-to)363-391
Number of pages29
JournalApplied Categorical Structures
Issue number1
Publication statusPublished - Feb 2011
Externally publishedYes


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