Functors of Complexes
Identifieur interne : 001C69 ( Main/Merge ); précédent : 001C68; suivant : 001C70Functors of Complexes
Auteurs : Albrecht Dold [Allemagne]Source :
- Classics in Mathematics [ 1431-0821 ] ; 1995.
Abstract
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 tℤ=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.
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DOI: 10.1007/978-3-642-67821-9_6
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<front><div type="abstract" xml:lang="en">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 tℤ=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.</div>
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