Algebraic Topology · Problem 3.1.7

Cohomology — Allen Hatcher

Mathematics — Topology · hom-homology-not-cohomology-theory

Problem

Show that the functors hn(X)=Hom(Hn(X),Z)h^n(X) = \text{Hom}(H_n(X), \mathbb{Z}) do not define a cohomology theory on the category of CW complexes.

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