Localization of homotopy epimorphisms and homotopy monomorphisms
Let \(f : X \to Y\) be a map between pointed connected CW-complexes and \(f_p : X_p \to Y_p\) be its \(p\)-localization, where \(p\) is either a prime or 0. It is shown that if \(X_p\) and \(Y_p\) are nilpotent and \(f\) is a homotopy epimorphism (monomorphism which is \(\text{mod } p\) nilpotent), then \(f_p\) is a homotopy epimorphism (monomorphism). For \(p = 3\), an example is constructed of a homotopy monomorphism \(f : X \to Y\) such that \(X_p\) and \(Y_p\) are nilpotent but \(f_p\) is not a homotopy monomorphism.
scientific article; zbMATH DE number 817787
scientific article