The realization of Verdier quotients as triangulated subfactors

Li, Zhiwei

doi:10.48550/arxiv.1612.08340

2016

DOI: 10.48550/arxiv.1612.08340

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The realization of Verdier quotients as triangulated subfactors

Zhiwei Li¹

Abstract: We give a method to realize Verdier quotients as triangulated subfactors of an arbitrary triangulated category. We show that Iyama-Yoshino triangulated subfactors are Verdier quotients under suitable conditions.

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Cited by 2 publications

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A homotopy theory of Nakaoka twin cotorsion pairs

Li¹

2017

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A homotopy theory of Nakaoka twin cotorsion pairs

Li¹

2017

Preprint

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Abelian categories from triangulated categories via Nakaoka-Palu's localization

Ogawa¹

2020

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The aim of this paper is to provide an expansion to Abe-Nakaoka's heart construction of the following two different realizations of the module category over the endomorphism ring of a rigid object in a triangulated category: Buan-Marsh's localization and Iyama-Yoshino's subfactor. Our method depends on a modification of Nakaoka-Palu's HTCP localization, a Gabriel-Zisman localization of extriangulated categories which is also realized as a subfactor of the original ones. Besides of the heart construction, our generalized HTCP localization involves the following phenomena: (1) stable category with respect to a class of objects; (2) recollement of triangulated categories; (3) recollement of abelian categories under a mild assumption.

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The realization of Verdier quotients as triangulated subfactors

Abstract: We give a method to realize Verdier quotients as triangulated subfactors of an arbitrary triangulated category. We show that Iyama-Yoshino triangulated subfactors are Verdier quotients under suitable conditions.

Cited by 2 publications

References 8 publications

A homotopy theory of Nakaoka twin cotorsion pairs

A homotopy theory of Nakaoka twin cotorsion pairs

Abelian categories from triangulated categories via Nakaoka-Palu's localization

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