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chain homotopy

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  • 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

  • Chain complex — Bicomplex redirects here. For the number, see Bicomplex number In mathematics, chain complex and cochain complex are constructs originally used in the field of algebraic topology. They are algebraic means of representing the relationships between …   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

  • Weak equivalence — In mathematics, a weak equivalence is a notion from homotopy theory which in some sense identifies objects that have the same basic shape . This notion is formalized in the axiomatic definition of a closed model category.Formal definitionA closed …   Wikipedia

  • Verdier duality — In mathematics, Verdier duality is a generalization of the Poincaré duality of manifolds to spaces with singularities. The theory was introduced by Jean Louis Verdier (1965), and there is a similar duality theory for schemes due to Grothendieck.… …   Wikipedia

  • Homotopie (homologische Algebra) — Im mathematischen Teilgebiet der homologischen Algebra ist eine Homotopie eine Abstraktion des topologischen Begriffes einer Homotopie. Definition Es seien X und Y Kokettenkomplexe und zwei Kettenabbildungen, d.h. Systeme von Abbildungen , die… …   Deutsch Wikipedia

  • Цепной комплекс — основное понятие гомологической алгебры. Содержание 1 Цепной комплекс 2 Коцепной комплекс 3 …   Википедия

  • Singular homology — In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of topological invariants of a topological space X , the so called homology groups H n(X). Singular homology is a particular example of a… …   Wikipedia

  • 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

  • Spectral sequence — In the area of mathematics known as homological algebra, especially in algebraic topology and group cohomology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a… …   Wikipedia

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