arXiv:1206.3850 Cohomology of algebras over weak Hopf algebras from arXiv Front: math.CT by J. N. Alonso Alvarez, J. M. Fernandez Vilaboa, R. Gonzalez Rodriguez In this paper we present the Sweedler cohomology for a cocommutative weak Hopf algebra H. We show that the second cohomology group classifies completely the weak crossed products, with a common preunit, of H with a commutative left H-module algebra A.
nLab page on Sweedler cohomology