Ramified Galois covers via monoidal functors

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 étale 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.