Localization of Nilpotent Groups and Spaces

1-connected 10calization abelian group admits an H-space apply arbitrary argue by induction assertion assume canonical map category NH cofibre commutative diagram connected CW-complex Corollary CW-complex Definition denote examples exists fact fibration fibre fibre-homotopy finite complex finite H-spaces finite type finitely-generated functor Fundamental Theorem genus H-complex H-map H-space structure H-structure hence homology homomorphism homotopy category homotopy equivalence homotopy groups homotopy theory homotopy type homotopy-commutative Hºx induced injective isomorphism Lemma Let f Let G localization of nilpotent localization theory map f nil G nilpotent CW-complex nilpotent groups nilpotent spaces non-cancellation operates nilpotently P-bijective P-equivalence P-injective P-isomorphism P-local P-surjective Postnikov system principal G-bundles principal refinement proof of Theorem Proposition 1.7 pullback Q-action quasifinite rationalization result Section Serre class short exact sequence ſix subgroup surjective Theorem Theorem 1B Theorem 2.9 trivial