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1 results

  • 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.