@Slereah I don't even know what $\mathbb{R}^{1|0}$ is :p page 1
here says it's completely legitimate to ignore all of these issues, at the end of the day the formal definitions are just a game to end up with whatever is done the normal way, I can't imagine the bundle/sheaf interpretation of local fermionic variables and black holes related to them, but the normal way will get there without thinking