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math.CT2021
Varieties of ordered algebras as categories
Jiří Adámek, Jiří Rosický
A variety is a category of ordered (finitary) algebras presented by inequations between terms. We characterize categories enriched over the category of posets which are equivalent…
cs.LO2021
Algebraic cocompleteness and finitary functors
Jiri Adamek
A number of categories is presented that are algebraically complete and cocomplete, i.e., every endofunctor has an initial algebra and a terminal coalgebra. For all finitary (and,…
math.CT2021
Reiterman's Theorem on Finite Algebras for a Monad
Jiri Adamek, Liang-Ting Chen, Stefan Milius +1
Profinite equations are an indispensable tool for the algebraic classification of formal languages. Reiterman's theorem states that they precisely specify pseudovarieties, i.e.~cla…