Two Ways to Centralizers of Equivalence Relations

摘要

We investigate what is the common part of the action accessible and the fibrewise algebraically cartesian closed (facc) categories dealing with the existence of centralizers of equivalence relations. Doing this, we shall introduce some new aspects of the Beck-Chevalley commutation with respect to the fibration of points and shall characterize the existence of those centralizers by a specific property of this same fibration.