Semilocalization of endomorphisms in homotopy theory (Q1295222)

Given a set of primes \(P\), Bendersky's semilocalization, applied to a space \(X\), is a universal map \(X\to X^{-}_{P}\) which preserves the fundamental group and \(P\)-localizes all higher homotopy groups. In the case where \(P\) is a single prime, the authors give conditions under which this map preserves a homotopy epimorphism, resp. a homotopy monomorphism.