On Key Relations Preserved by a Weak Near-Unanimity Function

In the paper we introduce a notion of a key relation, which almost coincides with the notion of a critical relation introduced by Keith A. Kearnes and Ágnes Szendrei. We show that we need only key relations to describe all clones on finite sets. We describe the set of all key relations on 2 elements, this set consists of all relations that can be defined as a disjunction of linear equations. Then we show that in general key relations do not have such a nice characterization, but we can get a characterization of key relations preserved by a weak near unanimity function.