Codepth Two and Related Topics

A depth two extension A | B is shown to be weak depth two over its double centralizer V A (V A (B)) if this is separable over B. We introduce a notion of codepth two coalgebra homomorphism g : C → D, dual to a depth two algebra homomorphism. It is shown that the endomorphism ring of bicomodule endomorphisms End D C D forms a right bialgebroid over the centralizer subalgebra g * : D * → C * of the dual algebra C * .