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In mathematics a stack or 2-sheaf is a sheaf that takes values in categories rather than sets.

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Grothendieck construction on fibred categories/stacks

The category $\operatorname{Stack}_{\mathcal C}$ of stacks in groupoids over $\mathcal C$ is a subcategory. By a result of Street, $\operatorname{Stack}_{\mathcal C}$ has all lax colimits. …
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