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Hovey M. Ч Model categories
Hovey M. Ч Model categories

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Ќазвание: Model categories

јвтор: Hovey M.

язык: en

–убрика: ћатематика/јлгебра/“еори€ категорий/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1999

 оличество страниц: 213

ƒобавлена в каталог: 20.04.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$f \Box g$      81 108
$K_\ast$      see also Уk-spaces pointedФ
$\Delta [n]$      75
$\Delta$      see also УSimplicial categoryФ
$\lambda$-sequence      see also УLambda sequenceФ
$\Lambda^r [n]$      75
$\mathcal{C}$-algebra      104
$\mathcal{C}$-algebra functor      104
$\mathcal{C}$-algebra natural transformation      104
$\mathcal{C}$-algebra structure      104
$\mathcal{C}$-model category      101 114 118
$\mathcal{C}$-module      104
$\mathcal{C}$-module functor      104
$\mathcal{C}$-module natural transformation      104
$\mathcal{C}$-module structure      104
$\mathcal{C}$-Quillen functor      114
$\mathrm{A}^\bullet \otimes \mathrm{K}$      76
$\mathrm{A}^\bullet \wedge \mathrm{K}$      76
$\partial \Delta [n]$      75
$\textrm{Cat}_{ad}$      see also У2-category of
$\textrm{SSet}_\ast$      see also УSimplicial sets pointedФ
$\textrm{Top}_\ast$      see also УTopological spaces pointedФ
$\textrm{T}_\ast$      see also УTopological spaces compactly pointedФ
$| - |$      see also УGeometric realizationФ
2-category      15 22 23 24Ч26
2-category of $\mathcal{C}$-algebras      105
2-category of $\mathcal{C}$-model categories      114
2-category of $\mathcal{C}$-modules      104
2-category of categories      18 24
2-category of categories and adjunctions      24
2-category of central $\mathcal{C}$-algebras      106
2-category of central monoidal $\mathcal{C}$-algebras      115
2-category of closed monoidal categories      107
2-category of closed monoidal pre-triangulated categories      174
2-category of model categories      18 24 191
2-category of monoidal $\mathcal{C}$-model categories      115
2-category of monoidal categories      103
2-category of monoidal model categories      113
2-category of pointed model categories      145
2-category of pre triangulated categories      172
2-category of stable homotopy categories      184
2-category of stable model categories      176
2-category of symmetric $\mathcal{C}$-algebras      105
2-category of symmetric monoidal $\mathcal{C}$-algebras      115
2-category of symmetric monoidal categories      104
2-category of triangulated categories      176 2
2-category, model      191 194
2-functor      24
Acyclic chain complex      see also Уchain complex acyclicФ
Adjunction of two variables      106 116 119
Anodyne extension      79 80Ч83 109
Associativity isomorphism      134
Basepoint      4
Bimodules      102Ч103 106
Bisimplicial sets      128Ч129 131Ч132
Boundary map      87 88 156 170
Brown, Ken      see also УKen Brown's lemmaФ
C*-algebras      192
Cardinal      28
Cardinal, $\gamma$-filtered      29
Cardinality argument      45
Category of simplices of a simplicial set      75 124
Central $\mathcal{C}$-algebra      105
Central $\mathcal{C}$-algebra functor      106
Central monoidal $\mathcal{C}$-model category      118
Ch(B)      see also УChain complexes of
Ch(R)      see also УChain complexes of
Chain complex, acyclic      41
Chain complexes of abelian groups      114 143Ч145 192
Chain complexes of comodules      28 60Ч72 112 114 176 188 194
Chain complexes of modules      27 40 41Ч48 111Ч112 114 176 183 188 194
Chain homotopy      43
Chain map      40
Closed $T_1$ inclusion      49
Closed monoidal category      106
Closed monoidal functor      106
Closed monoidal structure      106
Closed symmetric monoidal category      63 77
Cofiber      147
Cofiber sequence      147 151 156 157Ч165 169 177Ч182
Cofibrant      4
Cofibrant replacement functor      5
Cofibration      3
Cofibration, generating      34
Cofibration, trivial      3
Cofibration, trivial, generating      34
Cofinality of a cardinal      29
Cogroup object      151
Cogroup structure      150 151
Cogroup structure on $\Sigma X$      151
Cohomology functor      184 195
Colimit, homotopy      185 195
Colimit, sequential      185 195
Commutative monoid      192Ч193
Comodule      61
Comodule, cofree      63
Comodule, injective      63Ч65
Comodule, simple      61
Comodules      102 105
Comonad      193
Compactly closed      58
Compactly open      58
Correspondence of homotopies      150
Cosimplicial frame      127 128 130Ч139 144 167Ч169
Cosimplicial frames map of      127
Cosimplicial identities      73
Cosimplicial object      73 76
Cosmall      34
Cotriple      193
Cube lemma      126 153 158 161 166 168
CW-complex      51
Cylinder object      8 9 127 152Ч153
Deformation retract      53
Degeneracy map      73
Degeneracy of a simplex      74
Degree function      124
Derived adjunction      18
Derived functor, total left      16 17Ч22
Derived functor, total right      16
Diagonal functor      128Ч129 131Ч132
Dimension of a simplex      73
Direct category      119 120 121Ч124
double      165
Dual model category      4
Duality 2-functor      24 107 115 118 122 126 127 170 173
Dwyer, Bill      1 119
Equivalence in a 2-category      24
Exact adjunction      172 181
Face map      73
Face of a simplex      74
Fiber      148
Fiber homotopy equivalence      89 90Ч91
Fiber sequence      147 151 156 157Ч165 169 177Ч182
Fibrant      4
Fibrant replacement functor      5
Fibration      3
Fibration, Kan      79
Fibration, locally trivial      89 92Ч93 95Ч97
Fibration, minimal      89 91 92Ч95 97
Fibration, trivial      3
finite      29 187
Framing      119 123 127 128Ч129 131Ч145
Franke, Jens      195
Frobenius ring      36 37Ч40 71Ч72 112
Frobenius ring, Noetherian      39
Function complex      128
Function complex of simplicial sets      77
Functor, monoidal      see also УMonoidal functorФ
Functorial factorization      2 15 16 28
Geometric realization      77 78Ч81 85 95Ч99 102 114 118
Geometric realization, preserves fibrations      97
Geometric realization, preserves finite limits      80
Geometric realization, preserves products      77
Goerss, Paul      193
Group object      151
Group ring      36
Group structure      151
Group structure on $\Omega X$      151
Hirschhorn, Phil      x 1
Homology of a chain complex      41
Homotopic maps      9
Homotopy category      7
Homotopy equivalence      9 11
Homotopy groups of a chain complex of comodules      65
Homotopy groups of a fibrant simplicial set      83 85 86Ч89 97Ч99
Homotopy groups of a topological space      50
Homotopy of continuous maps      50
Homotopy of simplicial maps      86
Homotopy of vertices      84
Hopf algebra      36 60 112
Hopkins, Mike      193
Horizontal composition in a 2-category      23
Horizontal composition of natural transformations      18 23
Hurewicz cofibration      191
Hurewicz fibration      96 192
I-cell      see also УRelative I cell complexФ
I-cell complex      31
I-cofibration      30
I-fibration      30
I-injective      30
I-projective      30
Inclusion of topological spaces      49
Injective model structure      44 112
Inverse category      119 120 121Ч124
Johnson, Mark      x
K      see also Уk-spacesФ
k-small      29
k-space      58
k-spaces      77 80 98 106 111 114 118
k-spaces, pointed      111 114 118 176
Kan, Dan      x 1 3 119 194
Kelley space      see also Уk-spaceФ
Ken Brown's lemma      6 11Ч12 14 131Ч132 136
Lambda sequence      28
Latching space      120 122 124
Left exact      172
Left homotopy      9
Left homotopy between right homotopies      149
Left lifting property      3
Lewis, Gaunce      x
Limit, homotopy      175 185 186 195
Linear extension      120
Localizing subcategory      184 195
Loop functor      148 149Ч174 176Ч177 179Ч183
Mapping cylinder      165 167
Matching space      120 122 124
May, Peter      184 193
McClure, Jim      192
MOD      see also У2-category of
Model category      3
Model category, cofibrantly generated      27 34 35Ч36 108Ч109 123 183 185 187
Model category, fibrantly generated      34
Model category, finitely generated      34 175 184 187Ч190
Model category, pointed      4 14 15 21 26 36 115 144Ч145 147Ч174 185Ч190 195
Model category, simplicial      101 114 119 128 136 138Ч139 142Ч145 194
Model category, simplicial, pointed      115
Model category, stable      175 176 185 194
Model structure      3
Model structure, product      4 7 14 19
Module over a monoidal category      see also У$\mathcal{C}$-moduleФ
Modules over a Frobenius ring      27
Monad      193
Monoidal $\mathcal{C}$-model category      115 118
Monoidal $\mathcal{C}$-Quillen functor      115
Monoidal category      101 102
Monoidal functor      102
Monoidal model category      101 109 110Ч119 140Ч145
Monoidal model category, pointed      145 173Ч174
Monoidal model category, stable      176
Monoidal model category, symmetric      110Ч118
Monoidal natural transformation      103
Monoidal Quillen adjunction      113
Monoidal Quillen functor      113 141
Monoidal structure      102
Natural transformation monoidal, total derived      16 18 22
Non-degenerate simplex      74
Octahedral axiom      160Ч161 170 177
Operads      193
Ordinal      28 120
p-related vertices      91 93
Palmieri, John      x
Paracompact      96
Path component of a simplicial set      85
Path object      8 9
Pre-triangulated category      147 169 170 171Ч174 183 194
Pre-triangulated category, closed central monoidal      173
Pre-triangulated category, closed monoidal      173 174
Pre-triangulated category, closed symmetric monoidal      173
Pre-triangulation      169 170
Pseudo-2-functor      18 22 24 101 115 117Ч118 136 138 140Ч141 143 145 173Ч174 184 195
Pseudo-2-functor, homotopy      25
Pseudo-2-functor, natural isomorphism of      137
Pushout product      108 109
q      see also УCofibrant replacement functorФ
Quillen adjunction      14 15Ч22 35 71 131 136Ч139 163 191
Quillen adjunction of two variables      107
Quillen bifunctor      108 109Ч116
Quillen equivalence      13 19 20Ч22 26 48 98 191
Quillen functor      35 48 123 128 163Ч165
Quillen functor, left      13 14Ч19
Quillen functor, monoidal      see also УMonoidal Quillen functorФ
Quillen functor, right      14 15Ч19
Quillen, Daniel      1Ч195
R      see also УFibrant replacement functorФ
Reedy category      119 123 124 125Ч127 195
Reedy model structure      126 127 130 133 144 167
Reedy scheme      195
reflect      21
Relative I-cell complex      30 31Ч36
Retract argument      5
Rezk, Charles      x 191 193
Right exact      172
Right homotopy      9
Right homotopy between right homotopies      149
Right lifting property      3
Right proper      57
S-modules      113 176 184
Schwede, Stefan      49 109 194
Serre fibration      51 96 97
Shipley, Brooke      x
Sierpinski space      49
Simplicial category      73 119 123Ч125
Simplicial frame      127 128 130Ч133 144 163
Simplicial frames, map of      127
Simplicial identities      74
Simplicial object      73
Simplicial set, finite      74
Simplicial sets      73 74Ч101 109 114 118 119 128Ч145 188 192
Simplicial sets, pointed      98 100 110 114 118 176 183 185Ч187
Singular functor      77 98
Small      29 175 183 187Ч190
Small object argument      28 32 187
Smith, Jeff      x 107 109
SSET      see also УSimplicial setsФ
Stable category of modules      37
Stable equivalence of modules      36
Stable homotopy category      195
Stable homotopy category, algebraic      175 184
Stable homotopy category, algebraic, without duality      184
Stable homotopy category, ordinary      194
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