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Quasi-abelian hearts of twin cotorsion pairs on triangulated categories. (arXiv:1807.05423v1 [math.CT])
来源于:arXiv
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. 查看全文>>