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arXiv · 2510.25450

Stability Conditions on Abelian Comma Categories

Ellen de Oliveira·Guido Neulaender
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Abstract

A comma category, exemplified in algebraic geometry by coherent systems, combines two categories over a third through morphisms between their objects. We establish sufficient conditions for it to be abelian, compute its Grothendieck group, and give necessary and sufficient criteria for it to be noetherian and artinian. Finally, we define a stability condition on abelian comma categories under hypotheses on the initial categories and, conversely, induce stability conditions on the initial abelian categories from those on the comma categories.

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Ellen de Oliveira, Guido Neulaender. 2025-10-29. Stability Conditions on Abelian Comma Categories. https://arxiv.org/abs/2510.25450

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