2020/11/27 by Jiřı́ Adámek, Adámek, J., Matěj Dostál +3 · 1 citation
Computer Science · #18C15 #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2011.13839
openalex publication_date 2020/11/27 · openalex created_date 2020/12/07 · openalex updated_date 2026/07/28
It is well known that classical varieties of Σ-algebras correspond bijectively to finitary monads on Set. We present an analogous result for varieties of ordered Σ-algebras, i.e., classes presented by inequations between Σ-terms. We prove that they correspond bijectively to strongly finitary monads on Pos. That is, those finitary monads which preserve reflexive coinserters. We deduce that strongly finitary monads have a coinserter presentation, analogous to the coequaliser presentation of finitary monads due to Kelly and Power. We also show that these monads are liftings of finitary monads on Set.