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For questions about sheaves on a topological space.

11 votes
1 answer
1k views

Are groups determined by their morphisms from solvable groups?

$\newcommand{\Grp}{\mathrm{Grp}}$Consider the category of groups $\Grp$, and within it we have the solvable groups $S$. Then any group $G$ determines the functor from solvable groups: $$h_G:=\text{hom …
4 votes
1 answer
298 views

What extra structure does the group of automorphisms of a torsor carry?

Let $Y$ be a space, and $G$ a group. For simplicity we can take $G$ to be finite, $Y$ to be a point, if this avoids technical issues. Then for $X/Y$ a $G$ torsor, so a sheaf of sets with $G$ action on …