# 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.

## Key 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.

---
Source: https://tomesphere.com/paper/1703.08687