Equivalence for varieties in general and for \(\mathcal {BOOL}\) in particular
\textit{R. McKenzie} [in: A. Ursini et al. (eds.), Logic and algebra, Lecture Notes Pure Appl. Math. 180, 211-243 (1996; Zbl 0859.08006)] has characterized the varieties equivalent to a given variety in a purely algebraic fashion. The author of the paper under review characterizes the varieties \(\mathcal {W}\) equivalent to a variety \(\mathcal {V}\) in a purely categorical way. The varieties \(\mathcal {W}\) are described as the models of those Lawvere theories which are Morita equivalent to the Lawvere theory of \(\mathcal {V}\). As an application it is shown that the varieties \({\mathcal P}_m \) of Post algebras of fixed orders \(m\) are the only varieties equivalent to the variety \(\mathcal {BOOL}\) of Boolean algebras. The results are generalized to more general classes of algebras.
scientific article; zbMATH DE number 1899931