# Stacks associated to abelian tensor categories

@article{Liu2012StacksAT, title={Stacks associated to abelian tensor categories}, author={Yu-Han Liu and Hsian-hua Tseng}, journal={arXiv: Algebraic Geometry}, year={2012} }

For an abelian tensor category a stack is constructed. As an application we show that our construction can be used to recover a quasi-compact separated scheme from the category of its quasi-coherent sheaves. In another application, we show how the "dual stack" of the classifying stack $BG$ of a finite group $G$ can be obtained by altering the tensor product on the category $\rep{G}$ of $G$-representations. Using glueing techniques we show that the dual pair of a $G$-gerbe, in the sense of [TT10…

## 3 Citations

Tensor categorical foundations of algebraic geometry

- Mathematics
- 2014

Tannaka duality and its extensions by Lurie, Sch\"appi et al. reveal that many schemes as well as algebraic stacks may be identified with their tensor categories of quasi-coherent sheaves. In this…

Stacks and Torsors over Quivers

- Mathematics
- 2014

We study natural Grothendieck topologies on categories of quivers without and with relations, prove descent theorems for quiver representations, and introduce the notion of torsors over quivers.

Coherent Tannaka duality and algebraicity of Hom-stacks

- MathematicsAlgebra & Number Theory
- 2019

Australian Research CouncilAustralian Research Council [DE150101799]; Goran Gustafsson foundation; Swedish Research CouncilSwedish Research Council [2011-5599, 2015-05554]

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