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LECTURES ON DERIVED AND TRIANGULATED CATEGORIES

    https://doi.org/10.1142/9789812814333_0006Cited by:0
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    Abstract:

    The following sections are included:

    • Lecture 1: Abelian Categories

      • Products and Coproducts in Categories

      • Abelian Categories

      • Categories of Sheaves

      • Abelian Category of Quasi-Coherent Sheaves on a Scheme

      • Morita Equivalence of Rings

      • Appendix: Injective and Projective Objects in Abelian Categories

    • Lecture 2: Chain Complexes

      • Why Chain Complexes?

      • Chain Complexes

      • Constructions on Chain Complexes

      • Basic Properties of Cofiber Sequences

      • Derived Categories

      • Variations on the Theme of Derived Categories

      • Derived Functors

    • Lecture 3: Triangulated Categories

      • Triangulated Categories

      • Cohomological Functors

      • Abelian Categories Inside Triangulated Categories; t-Structures

      • Producing New Abelian Categories

      • Appendix I: Topological Triangulated Categories

      • Appendix II: Different Illustrations of TR4

    • Acknowledgments

    • References