How to construct a Hovey triple from two cotorsion pairs

2014/06/10 by Gillespie, James · 2 citations
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1406.2619

Abstract

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, \widetildeR) and (\widetildeQ, R) in A satisfying \widetildeR ⊆ R and Q ∩ \widetildeR = \widetildeQ ∩ R. We show how to construct a (necessarily unique) abelian model structure on A with Q (respectively \widetildeQ) as the class of cofibrant (resp. trivially cofibrant) objects and R (respectively \widetildeR) as the class of fibrant (resp. trivially fibrant) objects.

Cited by

• Induced complete hereditary cotorsion pairs in D(R) with respect to Cartan-Eilenberg exact sequences
• Models for chain homotopy category of relative acyclic complexes

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