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

Abstract

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.

arXiv comment30 pages, correction of minor errors, published in Appl. Categ. Structures

References in corpus (5)

• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• From triangulated categories to module categories via localisation II: Calculus of fractions
• Frobenius pairs in abelian categories: correspondences with cotorsion pairs, exact model categories, and Auslander-Buchweitz contexts
• From triangulated categories to module categories via localisation
• Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories

Cited by in corpus (2)

• A resolution theorem for extriangulated categories with applications to the index
• Localization of triangulated categories with respect to extension-closed subcategories