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arXiv · 1111.1820

General heart construction for twin torsion pairs on triangulated categories

Hiroyuki Nakaoka
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Abstract

In our previous article, we constructed an abelian category from any torsion pair on a triangulated category. This generalizes the heart of a $t$-structure and the ideal quotient by a cluster tilting subcategory. Recently, generalizing the quotient by a cluster tilting subcategory, Buan and Marsh showed that an integral preabelian category can be constructed as a quotient, from a rigid object in a triangulated category with some conditions. In this article, by considering a pair of torsion pairs, we make a simultaneous genralization of these two constructions.

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Hiroyuki Nakaoka. 2011-11-08. General heart construction for twin torsion pairs on triangulated categories. https://arxiv.org/abs/1111.1820

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