I have seen the grothendieck construction referenced in the literature several times, but never have found a good clean overview of how it works. How can I go from a stack which is a category fibered in groupoids over a site, let's say $(Sch/S)_{et}$, to a groupoid in $(Sch/S)$, and then back? For example, consider the quotient stack associated to the ramified etale cover $$ \text{Spec}(\mathbb{C}[x,y]/(x^5 - y)) \to \text{Spec}(\mathbb{C}[y]) $$ with isotropy group $\mathbb{Z}/5$ at the origin.
2026-02-23 02:59:30.1771815570
Where can I find a clear overview of the grothendieck construction?
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