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| Авторизация |
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| Gelfand S.I., Manin Yu.I. — Methods of Homological Algebra |
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| Предметный указатель |
Abelian group filtered 117
Abelian group filtered, simplicial 46
Abelian group filtered, topological 118
Additivity of the derived category 162
Affine group scheme 83
Bialgebra 83
Bisimplicial set 18
Boundary 29
Canonical decomposition of a morphism in an abelian category 112
Cap lower 240
Cap lower, upper 240
Cartier duality 85
Category 57
Category of an ordered set 60
Category of an ordered set, categories 67
Category of an ordered set, coindices 196
Category of an ordered set, complexes 58 168
Category of an ordered set, functors 63
Category of an ordered set, indices 86
Category of an ordered set, inductive limits 197
Category of an ordered set, projective limits 197
Category, abelian 113
Category, additive 113
Category, closed model 293
Category, cyclic 67
Category, derived 141
Category, dual 61
Category, exact 275
Category, examples of 58 59
Category, homotopic 159 246 332 354
Category, Probenius 276
Category, quotient 77
Category, simplicial 146
Category, stable 276
Category, triangulated 239
Chain 23
Chaindegenerate 53
Class complementary 291
Class complementaryof morphisms localizing 147
Class complementaryof morphisms localizing in a triangulated category 251
Class complementaryof morphisms, objects adapted to a functor 187
Classified space (of a group) 8 61
Coboundary 24
Cochain 24
Coefficient system 28
Coequalizer 88
Cofibration 293 331 335 350
Cohomology 47
Cohomology of a cochain complex 25 123
Cohomology of a cochain group 30
Cohomology of a cochain Lie algebra 48
Cohomology of a cochain sheaf 219
Cohomology of a cochain sheaf with the compact support 227
Cohomology, Cech 30 47
Cohomology, cyclic 54
Cohomology, Hochschild 54
Cokernel 111
Colimit 88
Complex of Cech 46
Complex, acyclic 123
Complex, bounded (from the left, from the right, from both sides) 147
Complex, chain 25
Complex, cochain 25 123
Complex, de Rham 48
Complex, de Rham, singular chains 47
Complex, diagonal 208
Complex, double 207 208
Complex, dualizing 234
Complex, K-injective 199
Complex, K-projective 199
Complex, Koszul 54 108
Complex, rigid 269
Complex, rigid, finite 269
Complex, twisted 262
Cone 26 154 244
Convolution of a complex 258
Core of a triangulated category 278
Coskeleton 16 93
CYCLE 25
Cylinder of a morphism 154
Cylinder of a morphism an object 332
Degeneration 14
Diagonal of a bisimplicial set 15
Differential graded algebra (DG-algebra) 338
Differential graded algebra, minimal 343
DIMENSION 227
Dimension, homological 171
Dimension, infective 172
Dimension, projective 172
Eilenberg — Zilber theorem 19
Element of an object of an abelian category 118
Epimorphism 114
Equilizer 87
Equivalence homotopic 301
Equivalence homotopic of categories 71
Equivalence homotopic of categories, examples 71—76
Equivalence, weak 293 331 334 350
Exact pair 215
Exact pair, sequence 40
Exact pair, sequence of cohomology 40
Exact pair, triple 40 42
Extension 257
Extension and  184
Extension by Yoneda 166
Face 14
Fiber of a sheaf in a point 34
Fibration 293 331 334 350
Fibration, locally trivial 321
Fibration, minimal 317
Fibration, universal 325
Filtration , regular 202
Filtration and  184
Filtration of a complex 203
Filtration of a complex, canonical 203
Filtration of a complex, stupid 203
Five-lemma 120
functor 60
Functor, additive 122
Functor, adjoint 89
Functor, cohomological 243
Functor, contravariant 61
Functor, covariant 61
Functor, derived 188
Functor, derived and  194
Functor, derived and ,  195
Functor, derived, classical 194
Functor, derived, of a composition 200
Functor, derived, weak 197
Functor, diagonal 86
Functor, exact 125 185 285
Functor, exact, from the left 125
Functor, exact, from the right 125
Functor, examples 60—62
Functor, faithful 64
Functor, forgetful 63 91
Functor, full 64
Functor, representable 78
Functor, representable in a category of sheaves 229
Geometrical realization 6
Geometrical realization of a simplicial topological space 18
Germ of a section 34
Gluing 1 288
Gluing data 1
Grassmann algebra 267
Grothendieck topology 100
Group cosimplicial 46
Group cosimplicial in a category 82
Group cosimplicial, simplicial 46
Hilbert theorem 175 176
| Homology 47
Homology of a chain complex 25 30
Homology of a group 30
Homology of a Lie algebra 48
Homology, cyclic 54
Homology, Hochschild 54
Homology, singular 47 50
Homotopy 49 53 107 301 333 351 353
Homotopy of a morphism of complexes 49 140
Homotopy of simplicial mappings 23
Homotopy of simplicial sets 301
Homotopy, group 356
Homotopy, group of a DG-algebra 353
Horn 294
Hypercohomology 213
Hypersimplex 260
Image 113
Image, direct 133
Image, direct with compact support 224
Image, direct with compact support, higher 227
Image, direct, higher 228
Image, inverse 134—136 223
Image, inverse, with compact support 228
Injectivity diagram 125
Isomorphism of triangles 157
Isomorphism of triangles, functors 69
Jordan — Holder theorem 122
Kan set 299
Kernel 111
Lie superalgebra 344
Limit, inductive 88 197
Limit, projective 86
localization 145
Manifolds 93
Massey product 266
Meier — Vietoris theorem 236
Minimal model of a de Rham algebra 352
Minimal model of a de Rham algebra DG-algebra 347
Mittag — Lefler condition 198
Module flat 128 217
Monomorphisms 114
Morita equivalence 77
Morphism 57
Morphism of coefficient systems 44
Morphism of complexes 41
Morphism of functors 63
Morphism of functors, examples 63
Morphism of sheaves 32
Morphism of spectral sequences 202
Morphism of triangles 157
Morphism, diagonal 80
Morphism, flat 128 224
Morphism, inner 105 108
Morphism, proper 224
Nerve of a category 104
Nerve of a category, covering 7
Object 57
Object, A-acyclic 133
Object, cofibrant 332
Object, F-acyclic (for functor F) 195
Object, fibrant 332
Object, final 65
Object, initial 65
Object, injective 125 275
Object, projective 125 275
Object, representing 78
Object, simple 121
Object, zero 110
Octahedron diagram 240
Poincare duality 234
Polycategory 65
Postnikov system 257
Presheaf 32 100
Product direct 80
Product direct, fiber 80
Projectivity diagram 128
Quadratic algebras 108
Quasi-isomorphism 143
quiver 288
Quotient category 77
Quotient category, (a la Serre) 121
Resolution, Cartan — Eilenberg 207
Resolution, flat 217
Resolution, free 139
Resolution, injective 143 179 199
Resolution, projective 141 199
Retraction 292
Ringed space 97
Roof 151
Scheme 98
Scheme, affine 95 97
Section of a sheaf 32
Section of a sheaf with compact support 225
Section of a sheaf with compact support in a subset 234
Sheaf 32
Sheaf of morphisms 38
Sheaf on a site 100
Sheaf, associated to a presheaf 35 114
Sheaf, constant 35
Sheaf, fine 38
Sheaf, flabby 37 219
Sheaf, flat 222
Sheaf, injective 218
Sheaf, locally constant 36
Sheaf, quasicoherent 40
Sheaf, soft 38 226
Sieve 100
Sieve, covering 100
Simplex n-dimensional 2 6
Simplex n-dimensional, non-degenerate 9
Simplex n-dimensional, singular 7
Simplices g-connected 316
Simplicial set 6
Simplicial set, N-truncated 16
Simplicial set, singular 60
Simplicial topological space 17
Site 100
Skeleton 3 13 92
Snake-lemma 120
Spectral sequence 201
Spectral sequence of a composition of functors 207
Spectral sequence of a double complex 207
Spectral sequence of a filtered complex 203 217
Spectral sequence of Cech cohomology 214
Spectral sequence of Eilenberg — Moore 263
Spectral sequence of hypercohomology 213
Spectral sequence of Serre — Hochschild 214
Spectral sequence, degenerate 202
Sphere simplicial 2 295
Square cartesian 81
Square cartesian, cocartesian 81
Subcategory 64
Subcategory, full 64 76
Subcategory, localizing 153
Subcategory, thick 266
Sum amalgamated 81
Sum, direct 138
Superspace 98
Suspension 276
Syzygies 139
t-structure 276 286
Tensor product of algebras 82
Translation functor 157 239
triangle 156
Triangle, distinguished 157 239
Triangulated space 2
Triangulation 2
Triangulation, canonical of the product of two simplices 4
Truncation functor 279
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