Ramified Galois covers via monoidal functors

Abstract: We interpret Galois covers in terms of particular monoidal functors, extending the correspondence between torsors and fiber functors. As applications we characterize tame $G$-covers between normal varieties for finite and \'etale group schemes and we prove that, if $G$ is a finite, flat and finitely presented nonabelian and linearly reductive group scheme over a ring, then the moduli stack of $G$-covers is reducible.