The homotopy fiber of profinite completion

We show that the basepoint-component of the homotopy fiber of Sullivanʹs profinite completion map c :Y→Ŷ is always an H-space, provided Y is nilpotent of finite type. This observation allows for a reworking of the completion/rationalization approach to phantom map theory and leads to more direct, transparent proofs of various results in the recent literature on phantom maps.