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How to construct a Hovey triple from two cotorsion pairs

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Gillespie J.

Fundamenta Mathematicae

2015

tom 230

nr 3

281-289

Let 𝓐 be an abelian category, or more generally a weakly idempotent complete exact category, and suppose we have two complete hereditary cotorsion pairs $(𝒬,\widetilde{𝓡})$ and $(\widetilde{𝒬},𝓡)$ in 𝓐 satisfying $\widetilde{𝓡} ⊆ 𝓡$ and $𝒬 ∩ \widetilde{𝓡} = \widetilde{𝒬} ∩ 𝓡$. We show how to construct a (necessarily unique) abelian model structure on 𝓐 with 𝒬 (resp. $\widetilde{𝒬}$) as the class of cofibrant (resp. trivially cofibrant) objects, and 𝓡 (resp. $\widetilde{𝓡}$) as the class of fibrant (resp. trivially fibrant) objects.

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1 Fundamenta Mathematicae

1 Gillespie J.

1 2015

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How to construct a Hovey triple from two cotorsion pairs