A homotopy theory of Nakaoka twin cotorsion pairs

TL;DR

This paper develops a homotopy theory framework for Nakaoka twin cotorsion pairs in triangulated categories, showing how Verdier quotients can be realized as subfactors, with applications to Iyama-Yoshino subfactors.

Contribution

It introduces a homotopy theory approach to Nakaoka twin cotorsion pairs and demonstrates their relation to Verdier quotients and triangulated subfactors.

Findings

Verdier quotients can be realized as subfactors via homotopy theory.

Iyama-Yoshino subfactors are shown to be Verdier quotients under certain conditions.

The framework unifies aspects of homotopy theory and triangulated categories.

Abstract

We show that the Verdier quotients can be realized as subfactors by the homotopy theory of additive categories with suspensions developed in \cite{ZWLi2, 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.