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Homotopy Limits, Completions and Localizations
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 nilpotentExpand
Function complexes in homotopical algebra
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 (1.4Expand
Calculating simplicial localizations
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 simpficiafExpand
HOMOTOPY COMMUTATIVE DIAGRAMS AND THEIR REALIZATIONS
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 diagramExpand
FUNCTORS INVOLVING C.S.S. COMPLEXES
Relative categories: Another model for the homotopy theory of homotopy theories
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.
ABSTRACT HOMOTOPY.
  • D. M. Kan
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences…
  • 15 December 1955
The mod-p lower central series and the Adams spectral sequence
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 XExpand
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