Extended Galois theory and dissonant morphisms (Q1818633)

Let \(\mathcal C\) be a category (for which a Galois structure is given) and \(p:E\to B\) an effective descent morphism in \(\mathcal C\). In this paper the notion of weakly split object over \((E,p)\) is introduced and the category of such objects is described in terms of internal actions of the Galois (pregroupoid) \((E,p)\) with an additional structure. Various known results in categorical Galois theory are obtained as special cases. Finally an elaborate list of examples and applications is given.