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1 results

  • 8 - Hereditary Model Structures

  • James Gillespie, Ramapo College of New Jersey
  • Book:
    Abelian Model Category Theory
    Published online:
    19 December 2024
    Print publication:
    02 January 2025, pp 208-254

  • Summary

    This chapter defines and studies hereditary model structures and their homotopy categories. This includes the special case of projective and injective model structures. It is shown that the homotopy category of any hereditary model structure is equivalent to the stable category of a Frobenius category. Morphism sets in the homotopy category are characterized as Ext groups. Practical methods for constructing hereditary model structures are also given. The end of the chapter focuses on adjunctions and recollements between homotopy categories as well as conditions guaranteeing that the homotopy category of an hereditary model structure is compactly generated.