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For questions requesting examples of a certain structure or phenomenon

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Are there any interesting examples of geometric triangulated categories with the Jordan-Hold...

categories have the Jordan-Holder property $\mathbf{D}(\Bbb P^1)$ and $\mathbf{D}(\Bbb P^1/\Gamma)$ connected Calabi-Yau categories derived categories of curves of positive genus These are the only examples
Brian Fitzpatrick's user avatar