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2 results

  • 11 - Mixed Model Structures and Examples

  • James Gillespie, Ramapo College of New Jersey
  • Book:
    Abelian Model Category Theory
    Published online:
    19 December 2024
    Print publication:
    02 January 2025, pp 351-360

  • Summary

    This chapter shows how two suitably related abelian model structures induce a third “mixed” abelian model structure. The resulting mixed model structure shares the weak equivalences of one but the fibrations of the other. We characterize the cofibrations in the mixed model structure and give several examples of mixed abelian model structures on chain complexes.

  • 10 - Resolving Subcategories of K(A,M)

  • Amnon Yekutieli, Ben-Gurion University of the Negev, Israel
  • Book:
    Derived Categories
    Published online:
    15 November 2019
    Print publication:
    19 December 2019, pp 230-241

  • Summary

    We define K-injective and K-projective DG modules in K(A,M) and also K-flat DG modules in K(A). These constitute full triangulated subcategories of K(A,M), and we refer to them as resolving subcategories. The category K(A,M)inj of K-injectives in K(A,M) plays the role of the category J in the abstract of Chapter 8, and the category of K-projectives K(A,M)prj plays the role of the category P there. The K-flat DG modules are resolving for the tensor functor. Furthermore, we prove that the functors Q : K(A,M)inj → D(A,M) and Q : K(A,M)prj → D(A,M) are fully faithful.