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Let $\mathcal{A}$ be an abelian category, or more generally a weaklyidempotent complete exact category, and suppose we have two complete hereditarycotorsion pairs $(\mathcal{Q}, \widetilde{\mathcal{R}})$ and$(\widetilde{\mathcal{Q}}, \mathcal{R})$ in $\mathcal{A}$ satisfying$\widetilde{\mathcal{R}} \subseteq \mathcal{R}$ and $\mathcal{Q} \cap\widetilde{\mathcal{R}} = \widetilde{\mathcal{Q}} \cap \mathcal{R}$. We showhow to construct a (necessarily unique) abelian model structure on$\mathcal{A}$ with $\mathcal{Q}$ (respectively $\widetilde{\mathcal{Q}}$) asthe class of cofibrant (resp. trivially cofibrant) objects and $\mathcal{R}$(respectively $\widetilde{\mathcal{R}}$) as the class of fibrant (resp.trivially fibrant) objects.

How to construct a Hovey triple from two cotorsion pairs