Abstract Let $$f :X \rightarrow Y$$ f : X → Y be a morphism of concentrated schemes. We characterize f -perfect complexes $${\mathscr {E}}$$ E as those such that the functor {E}}\otimes ^{\varvec{\texts...

Let h be a connective homology theory. We construct functorial relative plus construction as Bousfield localization functor in the category of maps spaces. It allows us to associate pair (X,H), consisting connected space X and an h-perfect normal subgroup H fundamental group π1(X), h-acyclic map X→XH+h inducing quotient by on group. show that this is terminal among kill H. When ordinary theory ...