Quasi-abelian hearts of twin cotorsion pairs on triangulated categories
arXiv:1807.05423 · doi:10.1016/j.jalgebra.2019.06.011
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.
23 pages, to appear in Journal of Algebra (available online: https://doi.org/10.1016/j.jalgebra.2019.06.011)
References in corpus (1)
Cited by in corpus (5)
- Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories
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- Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories
- The index with respect to a rigid subcategory of a triangulated category
- Examples and non-examples of integral categories and the admissible intersection property