Completions and localizations.- The R-completion of a space.- Fibre lemmas.- Tower lemmas.- An R-completion of groups and its relation to the R-completion of spaces.- R-localizations of nilpotent… Expand

1 .l Summary IN [l] QUILLEN introduced the notion of a model category (a category together with three classes of maps: weak equivalences, fibrations and cofibrations, satisfying certain axioms (1.4… Expand

1.1. Summary. This paper is essentially a continuation of [3], where we introduced a (standard) simplicial localization functor, which assigned to every category C and subcategory W c C, a simpficiaf… Expand

Abstract In this paper we describe an obstruction theory for the problem of taking a commutative diagram in the homotopy category of topological spaces and lifting it to an actual commutative diagram… Expand

We lift Charles Rezk's complete Segal space model structure on the category of simplicial spaces to a Quillen equivalent one on the category of relative categories.

USING A mod-p version of the lower central series one of us recently [lo] constructed a mod-p version of the spectral sequence of one of the others [3] and showed that for every topological space X… Expand