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arXiv · 2109.01395

Proper abelian subcategories of triangulated categories and their tilting theory

Peter Jorgensen
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Abstract

In the theory of triangulated categories, we propose to replace hearts of $t$-structures by proper abelian subcategories, which may be plentiful even when hearts are not. For instance, this happens in negative cluster categories. In support of our proposal, we show that proper abelian subcategories with a few vanishing negative self extensions permit a tilting theory which is a direct generalisation of Happel-Reiten-Smal{\o} tilting of hearts.

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BibTeXRIS

Peter Jorgensen. 2021-09-03. Proper abelian subcategories of triangulated categories and their tilting theory. https://arxiv.org/abs/2109.01395

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