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1 results

  • 2 - Cotorsion Pairs

  • James Gillespie, Ramapo College of New Jersey
  • Book:
    Abelian Model Category Theory
    Published online:
    19 December 2024
    Print publication:
    02 January 2025, pp 40-57

  • Summary

    This chapter studies cotorsion pairs in exact categories with a view toward developing the theory of abelian model structures. Basic concepts such as special precovers and complete cotorsion pairs are discussed. The more general notion of a complete Ext-pair is also introduced, and lifting and factorization properties for morphisms are developed. Hereditary cotorsion pairs are characterized and the Generalized Horseshoe Lemma is proved for hereditary cotorsion pairs. The special case of projective and injective cotorsion pairs is defined and characterized.