A Hovey triple arising from two cotorsion pairs

Abstract

Assume that $(\mathcal{C},\mathbb{E},\mathfrak{s})$ is an extriangulated category satisfying Condition (WIC). Let $(\mathcal{Q},\tilde{\mathcal{R}})$ and $(\tilde{\mathcal{Q}},\mathcal{R})$ be two hereditary cotorsion pairs satisfying conditions $\tilde{\mathcal{R}}\subseteq \mathcal{R}$, $\tilde{\mathcal{Q}}\subseteq \mathcal{Q}$ and $\tilde{\mathcal{Q}}\cap \mathcal{R}=\mathcal{Q}\cap \tilde{\mathcal{R}}$. Then there exists a unique thick class $\mathcal{W}$ for which $(\mathcal{Q},\mathcal{W},\mathcal{R})$ is a Hovey triple. As an application, this result generalizes the work by Gillespie in an exact case. Moreover, it highlights new phenomena when it applied to triangulated categories.

arXiv comment18 pages. arXiv admin note: text overlap with arXiv:1910.13278