Functors of Complexes

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


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.


Abelian Group Exact Sequence Natural Transformation Finite Type Additive Functor 
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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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