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arXiv · 1807.05423

Quasi-abelian hearts of twin cotorsion pairs on triangulated categories

Amit Shah
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Abstract

We prove that, under a mild assumption, the heart H of a twin cotorsion pair ((S,T),(U,V)) on a triangulated category C is a quasi-abelian category. If C is also Krull-Schmidt and T=U, we show that the heart of the cotorsion pair (S,T) is equivalent to the Gabriel-Zisman localisation of H at the class of its regular morphisms. In particular, suppose C is a cluster category with a rigid object R and [X_R] the ideal of morphisms factoring through X_R=Ker(Hom(R,-)), then applications of our results show that C/[X_R] is a quasi-abelian category. We also obtain a new proof of an equivalence between the localisation of this category at its class of regular morphisms and a certain subfactor category of C.

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BibTeXRIS

Amit Shah. 2019-06-23. Quasi-abelian hearts of twin cotorsion pairs on triangulated categories. https://doi.org/10.1016/j.jalgebra.2019.06.011

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