Let $Y$ be a complex algebraic variety, and let $n\in \mathbb Z_{\geq 1}\cup \{\infty\}$. How do I think about a proper $n$-etale morphism $X\to Y$?
If $n=1$, I think this should be a finite etale morphism (in the category of varieties).
If $n=2$, examples are $G$-gerbes over $Y$.
Do elements in $H^n(Y,G)$ give rise to proper $n$-etale morphisms $X\to Y$?