Hey y'all, here's a question about torsors: what's the qualitative difference between the two following "torsor conditions" for some topos, a group object $G$, a potential $G$-torsor $P$ and an object $B$ in that topos:
on one hand, we can ask for a relative torsor condition $P\times_B P\simeq P\times _B G$ versus $P\times_B P \simeq P\times G$?