Centrality and connectors in Maltsev categories

We develop a new approach to the classical property of centrality of equivalence relations. The internal notion of connector allows to clarify classical results in Maltsev varieties and to extend them in the more general context of regular Maltsev categories, hence including the important new examples of Maltsev quasivarieties and of topological Maltsev algebras. We also prove that Maltsev categories can be characterized in terms of a property of connectors.