# Chain functors with isomorphic homology

## Friedrich W. Bauer

Every chain functor ${\bf K}_{*}$ determines a homology theory on a given category of topological spaces resp. of spectra $H_{*}(\bf K_{*})(\cdot)$ cf. \S 4. If $\bf K_{*}$, ${\bf L}_{*}$ are chain functors such that $H_{*}({\bf K}_{*})(\cdot) \approx H_{*}({\bf L}_{*})(\cdot)$ then there exists a third chain functor ${\bf C}_{*}$ and transformations of chain functors ${}^{K}\gamma :{\bf K}_{*} \longrightarrow {\bf C}_{*}$, ${}^{L}\gamma:\ {\bf L}_{*} \longrightarrow {\bf C}_{*}$ inducing isomorphisms of the associated homology theories (theorem 1.1.). Moreover the distinction between regular and irregular chain functors is introduced.

Homology, Homotopy and Applications, Vol. 3, 2001, No. 2, pp. 37-53

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