Braided Galois objects and Sweedler cohomology of certain Radford biproducts

We construct the group of H-Galois objects for a flat and cocommutative Hopf algebra in braided monoidal category with equalizers provided that certain assumption on braiding is fulfilled. show it subgroup BiGalois Schauenburg, prove latter isomorphic to semidirect product automorphisms H objects. Dropping braiding, we normal basis. For Sweedler cohomology second Picard invertible H-comodules H. every object an H-comodule, yielding morphism from A short exact sequence constructed relating two groups, under above mentioned braiding. how our constructions generalize some results modules over commutative rings, other known symmetric categories. Examples algebras are discussed which compute Galois