How to construct a Hovey triple from two cotorsion pairs

• Autorzy: James Gillespie
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 18E10: Exact categories, abelian categories
• 18G25: Relative homological algebra, projective classes
• 55U35: Abstract and axiomatic homotopy theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 230
• Numer: 3
• Strony: 281-289

Daty

wydano

2015

Twórcy

autor

James Gillespie

• Ramapo College of New Jersey, School of Theoretical and Applied Science, 505 Ramapo Valley Road, Mahwah, NJ 07430, U.S.A.

Identyfikatory

DOI

10.4064/fm230-3-4