A homotopy theory of Nakaoka twin cotorsion pairs

2017/03/25 by Zhiwei Li, Li, Zhi-Wei
Mathematics · #18E30 #18E35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1703.08687

openalex publication_date 2017/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Verdier quotients can be realized as subfactors by the homotopy theory of additive categories with suspensions developed in \citeZWLi2, ZWLi3. As applications, we develop the homotopy theory of Nakaoka twin cotorsion pairs of triangulated categories and prove that Iyama-Yoshino triangulated subfactors are Verdier quotients under suitable conditions.

Citations

• Relative singularity categories, Gorenstein objects and silting theory

Related

• A homotopy theory of additive categories with suspensions
• The realization of Verdier quotients as triangulated subfactors
• Cotorsion pairs and model categories
• The triangulation of the subfactor categories of additive categories with suspensions
• Verdier quotients of homotopy categories