Minimal algebras and category equivalences
Tame congruence theory [\textit{R. McKenzie} and \textit{D. Hobby}: The structure of finite algebra (Contemp. Math. 76) (1988; Zbl 0721.08001)] distinguishes five types of minimal algebras. Three of them are two- element algebras. Two-element algebras and the varieties they generate have various interesting properties. The five types of minimal algebras create a new classification of two-element algebras, or, equivalently, of all clones of Boolean functions. Both approaches try to reduce the structure of finite algebras and locally finite varieties to simpler algebras and varieties they generate. The paper considers interconnections between these approaches.
scientific article; zbMATH DE number 21347
scientific article