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 $\mathcal X$ over $S$, one can define the Picard stack $\mathcal{Pic}_{\mathcal X/S}$. Is this a Picard stack as defined in "Smooth Toric Deligne-Mumford stacks" by Fantechi, Mann and Nironi?

Are Picard stacks group objects in the category (or 2-category?) of algebraic stacks?

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    @QiaochuYuan That actually answers my question. A monoidal groupoid in which every object is invertible is a 2-group. That's all I needed to hear. Thank you. – Christian Feb 16 '16 at 15:29

Converting my comment into an answer: stacks form a 2-category, not a category. If a stack takes values in groupoids, then a "group stack" takes values in 2-groups, or equivalently in monoidal groupoids where every object is invertible. But it's natural to go further and ask for "abelian group stacks," which take values in symmetric monoidal groupoids where every object is invertible (e.g. the symmetric monoidal groupoid of line bundles on a scheme). These groupoids are sometimes called Picard groupoids, and this notion of stack is sometimes called a Picard stack.

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