The derived category is made to emerge from a treatment of the long exact sequence in which mapping cones, quasi-isomorphisms and fractions emerge naturally. Simple homotopy properties avoid the need to introduce triangulated categories, although we do introduce them by way of connecting to standard approaches. We sketch how the derived category streamlines derived functor theory, provides a fundamental reinterpretation of cup products and new approach to duality theorems.

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Derived Categories via the Long Exact Sequence

  • John Rice

摘要

The derived category is made to emerge from a treatment of the long exact sequence in which mapping cones, quasi-isomorphisms and fractions emerge naturally. Simple homotopy properties avoid the need to introduce triangulated categories, although we do introduce them by way of connecting to standard approaches. We sketch how the derived category streamlines derived functor theory, provides a fundamental reinterpretation of cup products and new approach to duality theorems.