Internal bialgebroids, entwining structures and corings

Abstract

The internal bialgebroid -- in a symmetric monoidal category with coequalizers -- is defined. The axioms are formulated in terms of internal entwining structures and alternatively, in terms of internal corings. The Galois property of the coring in question is related to the $\times_R$-Hopf algebra property. The language of entwining structures is used to discuss duality.