Extended Galois theory and dissonant morphisms Original Research Article

For a given Galois structure on a category image and an effective descent morphism p : E→B in image we describe the category of so-called weakly split objects over (E,p) in terms of internal actions of the Galois (pre)groupoid of (E,p) with an additional structure. We explain that this generates various known results in categorical Galois theory and in particular two results of Barr and Diaconescu [1]. We also give an elaborate list of examples and applications.