Remark 3.51.
Under the equivalence \(T_{/\bB G} \simeq \Mod_G(T)\), passing to fibers over \(T\) (with respect to the forgetful functor \(T_{/\bB G} \to T\) and the quotient functor \(\Mod_G(T) \to T\)) yields
\[\Hom_T(*,\bB G) \;\simeq\; \{\text{$G$-torsors in $T$}\}^{\simeq} .\]