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Bousfield A., Kan D. — Homotopy limits, completions and localizations
Bousfield A., Kan D. — Homotopy limits, completions and localizations



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Название: Homotopy limits, completions and localizations

Авторы: 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: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1972

Количество страниц: 348

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
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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