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Functors of Complexes

  • Albrecht Dold
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 200)

Abstract

If T: ∂AG → ∂AG is a functor from complexes to complexes then X → TSX provides a generalization of the singular complex SX which may yield new useful topological invariants. We study this question (§§ 2–7), at least if T is the (dimension-wise) prolongation of an additive functor t: AG → AG. We find that for every abelian group G there is, essentially, one covariant and one contravariant t such that t ℤ = G. The resulting groups HTSX are the homology respectively cohomology groups of X with coefficients in G. The functors t are also useful in studying product spaces; these questions are discussed in §§ 8–12.

Keywords

Abelian Group Exact Sequence Natural Transformation Finite Type Additive Functor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1972

Authors and Affiliations

  • Albrecht Dold
    • 1
  1. 1.Mathematisches InstitutUniversität HeidelbergDeutschland

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