Category equivalences of clones

This note was inspired by McKenzie's recent paper [8] whose main result is a characterization of categorical equivalence (for short category equivalence) between varieties. Here we use this result to define category equivalent clones and to describe all clones category equivalent to maximal clones. If one is interested in maximal clones only up to category equivalence it is sufficient to consider very simple maximal clones, essentially the same as considered in Jablonski's early papers about maximal clones [6]. The results we have found encourage us in our feeling that category equivalence could be a useful tool in clone theory.Dedicated to the memory of Alan Day.Presented by J. Sichler.