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Bousfield A., Kan D. — Homotopy limits, completions and localizations
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Название: Homotopy limits, completions and localizationsАвторы: Bousfield A., Kan D. Аннотация: The main purpose of part I of these notes is to develop for a ring R a functional notion of R-completion of a space X. For R=Zp and X subject to usual finiteness condition, the R-completion coincides up to homotopy, with the p-profinite completion of Quillen and Sullivan; for R a subring of the rationals, the R-completion coincides up to homotopy, with the localizations of Quillen, Sullivan and others. In part II of these notes, the authors have assembled some results on towers of fibrations, cosimplicial spaces and homotopy limits which were needed in the discussions of part I, but which are of some interest in themselves.
Язык: Рубрика: Математика /Алгебра /Алгебраическая геометрия /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1972Количество страниц: 348Добавлена в каталог: 12.03.2005Операции: Положить на полку |
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Acyclic functor VII Acyclic functor R VII Artin — Mazur completion III Artin — Mazur completion, augment I X Base point VIII Closed (simplicial) model category VII VIII VIII x XI Codegeneracy 1 X XII Coface 1 X Cofibrant VIII X Cofibration VII VIII X XI Cofinality theorem XI Cohomology spectral sequence XII XII Cohomotopy X Complete convergence VI IX Complete r 1 VII Complete, Ext-p VI 3 Completion, Artin — Mazur III Completion, Ext VI VI VI Completion, Hom VI VI VI Completion, Malcev IV V Completion, p VI Completion, p-profinite IV VI Completion, R 1 IV IV XI Connectivity lemmas I IV Convergence complete VI IX Convergence, Curtis IV V VI Convergence, Mittag — Leffler V VI VII IX Core I I Core lemma I I Cosimplicial diagram XI Cosimplicial identities X Cosimplicial map I X Cosimplicial object X Cosimplicial replacement XI Cosimplicial resolution 1 XI Cosimplicial space 1 X Cosimplicial standard simplex 1 X Curtis convergence IV V VI Degeneracy VIII Degenerate VIII Degenerate, cosimplicial XI Degenerate, non VIII 2 Degenerate, simplicial XII Diagonal XII Diagram III XI 2 Direct limit XII XII Direct limit, homotopy XII Disjoint union lemma I Ext, completion VI 2 Ext, p-complete VI Face VIII Fibrant VIII X Fibration VII VIII X XI 8 Fibration, nilpotent II Fibration, nilpotent, lemma II Fibration, principal II Fibration, principal, lemma II III Fibre VIII Fibre space V Fibre type IV V Fibre, mod-R, lemma II III Fibre, square lemma II Fibre, wise R-completion I II IV VII Finite product lemma I Fracture lemmas V V VI Function space V VI VIII X XI Group-like X H-space I V Homology, reduced I Homology, spectral sequence XII Homotopy category III VIII VIII XI XII Homotopy, (pointed) set VIII Homotopy, class of maps VIII Homotopy, direct limit XII Homotopy, equivalence III Homotopy, group III Homotopy, inverse limit XI XI XI Homotopy, sequence IX Homotopy, spectral sequence i V VI VII IX X Homotopy, weak pro, equivalence III Homotopy, — relation VIII Horn completion VI Hurewicz homomorphism I Inverse limit IX IX XI XI XI Inverse limit, homotopy XI XI XI Large XI Left filtering III XI Left lifting property VIII Left, cofinal III XI Left, small XI localization VIII XI Localization, R V Lower (p)-central series IV IV VI Malcev completion IV V Matching space X Maximal augmentation X Mittag — Leffler IX Mittag — Leffler convergence V VI VII IX Mixing, Zabrodsky V mod-R fibre lemma II III XI Neighborhood group V VI Nilpotent action II III Nilpotent fibration II Nilpotent fibration lemma II Nilpotent group II Nilpotent space II Nilpotent, R III p-adic integers VI IX p-completion VI 6 p-profinite completion IV VI Perfect VII Perfect, R VII VII Pointed ... VIII Principal fibration II Principal fibration, lemma II III Pro isomorphism III III Pro object III Pro trivial III Pro, weak homotopy equivalence III Product, finite lemma I R-acyclic VII R-acyclic functor VII R-bad I IV VII r-complete I VII R-complete, semi VII 2 R-complete, tower lemma III R-completion I IV IV XI R-completion, fibre-wise I II IV R-completion, partial VII R-completion, semi VII 2 R-good I VII VII VII VII R-homotopy theory VII R-localization V R-nilpotent group III IV R-nilpotent space III R-nilpotent, tower lemma III IV R-perfect VII VII R-tower II1 IV Realization functor VIII Reduced homology I Reduced space IV Right filtering XII Right lifting property X simplex VIII Simplex, cosimplicial standard I X Simplex, standard VIII Simplicial diagram XII Simplicial identities VIII Simplicial map VIII Simplicial object III Simplicial replacement XII Simplicial set VIII Singular functor VIII Skeleton VIII Small III XI Small, left XI Solid ring I I I Space (= simplicial set) I Standard, cosimplicial simplex I X Standard, map VIII Standard, simplex VIII Total space i X Tower comparison lemma III Tower lemmas III IV Tower of fibrations IX Tower of groups III IX - Tower, R III IV Triple I XI Triple lemma I Unaugmentable X Underlying space XI Union, disjoint lemma I Universal properties VII XI XII Vertex VIII Weak equivalence VII VIII x XI Weak pro-homotopy equivalence III Z-nilpotent (= nilpotent) III Zabrodsky mixing V
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