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Moerdijk I. — Classifying Spaces and Classifying Topoi
Moerdijk I. — Classifying Spaces and Classifying Topoi



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Название: Classifying Spaces and Classifying Topoi

Автор: Moerdijk I.

Аннотация:

This monograph presents a new, systematic treatment of the relation between classifying topoi and classifying spaces of topological categories. Using a new generalized geometric realization which applies to topoi, a weak homotopy equival- ence is constructed between the classifying space and the classifying topos of any small (topological) category. Topos theory is then applied to give an answer to the question of what structures are classified by "classifying" spaces.
The monograph should be accessible to anyone with basic knowledge of algebraic topology, sheaf theory, and a little topos theory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 94

Добавлена в каталог: 07.12.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$Ab(\mathcal{E})$      15
$Hom\mathcal{(F,E)}$      7
$H^{n}\mathcal{(E,A)}$      16
$H^{\cdot}(C,A)$      43
$k_{C}(X)$      27 35 80 83
$Lin_{c}(X,C)$      43
$Lin_{c}(X,F)$      88
$SLC(\mathcal{E})$      18
$\Delta$      8
$\Delta^{n}$      58
$\Delta_{m}(C)$      63
$\gamma$      8
$\Gamma(M)$      36
$\Gamma^{q}$      83
$\mathcal{B}(\triangle^{op})$      40
$\mathcal{B}C$      11 28
$\mathcal{B}G$      21
$\mathcal{B}\triangle$      40
$\mathcal{D}C$      38 43
$\mathcal{I}C$      51
$\mathcal{S}$      58
$\mathcal{[F,E]}$      19
$\overline{\mathcal{B}}C$      54 69
$\pi_{0}$      17
$\pi_{n}(\mathcal{E},p)$      18
$\pi_{n}^{et}(\mathcal{E},p)$      18
$\Sigma$      59
$\triangle$      37
$|X|_{(J)}$      58
$|X|_{(\Sigma)}$      59
$||X||_{J}$      67
$||X||_{\Sigma}$      69
AB      15
Augmentation      39
Augmented bundle      39 40
AugPrin(X,K,Y)      39
Bc      60
Bousfield — Kan spectral sequence      50
Bundle, augmented      39
Bundle, C-      24
Classifying space      60
Classifying topos      11
Classifying topos of a topological category      29
Cohomology of a category      43
Cohomology of a topos      15
Colimits of topoi      13
Comma-category      8
Comparison between classifying topoi and classifying spaces      77 ff
Concordance classes      27 35 79 83
Concordant      27
Connected morphism      19
Connected object      17
Connected topos      17
Constant sheaf functor      8
Contractible Kan complex      17
Cosimplicial sets      40
Cosimplicial topos      66
Covering spaces      17 79
Deligne classifying topos      38 88
Descent data      29
Diaconescu’s theorem      24 28
Diagram of spaces      38 49
Direct image functors      7
Disjoint sum      5
Effective descent map      29
Equivalence between topoi      8
Equivalence of topological categories      30
Equivalence relation      6
Equivalent topoi      8
Essentially surjective      30
Etale homotopy groups      18
Etale map      8
Etale space      8
Exact diagram      6
Filtering      24
First vertex functor      60
Flat      24
Foliations      3 84
free      24
Fully faithful      30
Fundamental group      17 18
G-equivariant sheaves      28
Generate      7
Generators      7
Geometric realization of simplicial spaces      59
Geometric realization |X|      57
Giraud axioms      5
Global sections functor      8
Grothendieck spectral sequence      16
Haefliger groupoid      4
Holonomy groupoid      3
Homotopic      18
Homotopy classes of topos morphisms      19 23
Homotopy of a topos      15
Hurewicz Theorem      18
Hypercovers      16
Inductive limit of topoi      14
Inverse image functor      7
Invertible C-sheaf      51
Irreducible closed set      9
Leray spectral sequence      16
Lin(X)      40
Lin(X,Y)      42
Linear order      40
Linear order, C-augmented      88
Local homeomorphism      8
Locally acyclic      16
Locally connected      17 50 51
Locally connected topos      17
Locally constant objects      17
Locally contractible category      83
M      28
Monoid of smooth embeddings      83
Morphism between topoi      7
Morphism-inverting functors      79
Natural transformation      7
Nerve (C)      38
Prin(X,C)      25 32
Prin(X,G)      21
Prin(X,Y_{K})      39
Principal C-bundle      24
Principal C-bundles      3 32
Principal G-bundle      21
Products of topoi      15
Profinite fundamental group      17
Progroup      18
Projective resolution      44
Pseudo-constant object      75
Pseudo-constant sheaf      62 75 78
Pushout of topoi      13
Quasi-C-sheaf      54
Quillen’s Theorem A      61
Quillen’s Theorem A, topological version of      63
Representable presheaf      11
S      28
s-etale      31
s-etale topological category      31 80 81
Sets      8
Sh(X)      9
Sh(Y)      38 86
Sheaf      8
Sheaf, C-      28 51
Sheaves on a diagram      38
Sheaves on a simplicial space      38
Sierpinski homotopy      19
Sierpinski interval      67
Sierpinski realization      80
Sierpinski space      59
Simp(Y)      86
Simplicial model category $\triangle$      37
Simplicial object      16
Simplicial sets      40 57
Simplicial space      86
Small category      5
Sober      9
Stably exact      6
Standard n-simplex      58
SUM      5
Sum of topoi      13
Sum, disjoint      5
Sum, stable      6
t      28
Tensor product      25 66
Thickened geometric realization      59
Topological category      3 28 51 88
Topological groupoid      35
Topological version of Quillen’s Theorem A      63
Topos      5 50 55
Topos of presheaves      8
Topos of quasi-C-sheaves      55
Topos of sheaves on a space      8
Topos-theoretic realization      67
Toposophic Whitehead theorem      19
Transitive      24
Trivial fibration      16
U      28
Verdier cohomology      17
Weak homotopy equivalence      19 77 81
Yon      11
Yoneda embedding      11
Yoneda Lemma      11
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