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I've been wondering about what a "group algebraic stack" should be, and ran into the notion of a Picard stack. I'm slightly confused by the terminology here. Given an algebraic stack $\mathcal X$ ...

Suppose $S$ is a scheme, and $G$ a smooth $S$-group scheme. Then there exists an algebraic stack BG called the classifying stack of $G$, defined as the quotient stack $[S/G]$ where $G$ acts trivially ...