Some Classes of Centralizing Monoids on a Three-Element Set

Commutation is defined for multi-variable functions on a non-empty set A. A centralizing mooned M is a set of unary functions which commute with all members of some set F of multi-variable functions. In such a case, we call F a witness of M. In this paper, we consider the case where A is a three-element set and determine all centralizing monodies which have ternary majority functions or ternary semi projections as their witnesses.