Abstract: In the higher-categorical setting, Galois theory extends beyond finite groups: one can study Galois extensions for an arbitrary E_1-group. We develop such a theory for higher semiadditive categories, where finite groups are naturally replaced by pi-finite groups. Under suitable height assumptions, we construct an n-truncated pro-pi-finite "absolute Galois group" classifying all Galois extensions. We also relate abelian extensions to the Picard spectrum through a higher version of Kummer theory. Time permitting, we will compute the absolute Galois group in some chromatic and categorified settings.