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category of complexes

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  • Derived category — In mathematics, the derived category D(C) of an abelian category C is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on C. The construction proceeds on the… …   Wikipedia

  • Homotopy category of chain complexes — In homological algebra in mathematics, the homotopy category K(A) of chain complexes in an additive category A is a framework for working with chain homotopies and homotopy equivalences. It lies intermediate between the category of chain… …   Wikipedia

  • Differential graded category — In mathematics, especially homological algebra, a differential graded category or DG category for short, is a category whose morphism sets are endowed with the additional structure of a differential graded Z module. In detail, this means that… …   Wikipedia

  • Triangulated category — A triangulated category is a mathematical category satisfying some axioms that are based on the properties of the homotopy category of spectra, and the derived category of an abelian category. A t category is a triangulated category with a t… …   Wikipedia

  • Homotopy category — In mathematics, a homotopy category is a category whose objects are topological spaces and whose morphisms are homotopy classes of continuous functions. The homotopy category of all topological spaces is often denoted hTop or Toph.Homotopy… …   Wikipedia

  • Model category — In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ( arrows ) called weak equivalences , fibrations and cofibrations . These abstract from a conventional homotopy category, of… …   Wikipedia

  • Higher category theory — is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. Contents 1 Strict higher categories 2 Weak higher… …   Wikipedia

  • Exact category — In mathematics, an exact category is a concept of category theory due to Daniel Quillen which is designed to encapsulate the properties of short exact sequences in abelian categories without requiring that morphisms actually possess kernels and… …   Wikipedia

  • Glossary of category theory — This is a glossary of properties and concepts in category theory in mathematics.CategoriesA category A is said to be: * small provided that the class of all morphisms is a set (i.e., not a proper class); otherwise large. * locally small provided… …   Wikipedia

  • Mapping cone (homological algebra) — In homological algebra, the mapping cone is a construction on a map of chain complexes inspired by the analogous construction in topology. In the theory of triangulated categories it is a kind of combined kernel and cokernel: if the chain… …   Wikipedia

  • Hyderabad, Andhra Pradesh — {category|}Infobox Indian Jurisdiction type = metropolitan city type 2 = capital native name = Hyderabad nickname = The City of Pearls, The City of the Nizams. state name = Andhra Pradesh skyline = Hyderabad india .jpg skyline caption = Charminar …   Wikipedia

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