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Maclane S. — Homology
Maclane S. — Homology

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Название: Homology

Автор: Maclane S.

Аннотация:

In presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which I have had from all sides. Homological algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with Otto Schilling. A further development of homological ideas, with a view to their topological applications, came in my long collaboration with Samuel Eilenberg; to both collaborators, especial thanks. For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Указатель в процессе заполнения

ed2k: ed2k stats

Год издания: 1963

Количество страниц: 422

Добавлена в каталог: 30.08.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian category      254
Abelian group      10
Abstract category      28
Abstract kernel      124
Acyclic space      57
Additive bifunctor      71
Additive category      249
Additive functor      23 71 263 379
Additive relation      51 366
Adjoint Associativity      95 144 194
Adjoint, left      266 269
Affine independence      54
Affine simplex      54
Affine transformation      54
Alexander — Whitney map      241
Algebra      173
Algebra extension      284
Allowable class (in a category)      260
Allowable Comparison Theorem      261
Allowable exact sequence      261
Allowable injective      261
Allowable morphism      260
Allowable projective object      261
Allowable projective resolution      261 378
Allowable resolution      261
Analysis (of a morphism)      254
Annihilator      146
Anti-isomorphism      364
Associated graded modules      326
Associative law      173
Associative law for diagonal map      197
Associative law for tensor product      142 145 194
Associativity      25 249
Augmentation      180
Augmentation of DG-algebra      192
Augmentation of DG-module      304
Augmentation of graded algebra      180
Augmentation of group ring      104
Augmentation of singular complex      57
Augmented algebra      180
Automorphism      104
Automorphism class      124
Axioms for cohomology of algebras      287
Axioms for cohomology of groups      117
Axioms for Ext      99 101 269
Axioms for homology of algebras      289
Axioms for Tor      162 275
Baer sum      69 85 113
Bar construction      306
Bar resolution      115 268 271 280
Barycentric coordinates      54
Base (of spectral sequence)      321
Betti number      42 323
Biadditive function      138
Biadditive functor      400
Bidegree      176
Bifunctor      31 393
Bigraded algebra      180
Bigraded module      176
Bilinear function      141
Bimodule      143
Bimodule bar      282
Bimodule bar resolution      282
Bimodule tensor product      187
Binomial coefficient      183
Bockstein cohomology operator      49 339
Boundary      35 39 56
Boundary homomorphism      35 56 235
Bounded below (spectral sequence)      321
Bounded filtration      327 330
Canonical comparison      267
Canonical Comparison Theorem      267
Canonical map      11
Canonically bounded      330 346
Canonically bounded filtration      330
Cartesian product      18
Cartesian product of modules      18
Cartesian product of sets      8
Cartesian product of simplicial sets      238
Categorical bar      268 271
Category      25
Category of diagram      257
Category of sets      26
Cauchy's theorem      131
Center of a group      124
Central group extension      112
Chain      35
Chain complex      39
Chain equivalence      40
Chain homotopy      40
Change of algebras      289
Change of group      108
Change of groups      108
Change of ring      90 276
Change of rings      90 276 293
Characteristic class      120
class      26
Cleft extension      284
Coalgebra      197
Coboundary      42 43 116
Cobounded filtration      346
Cochain      42
Cochain complex      42
Cocycle      43
Codiagonal map      68 251
Codimension      218
Cohomology      42
Cohomology group      115
Cohomology of a group      115
Cohomology product      222 296
Coimage      12 41 255
Coinitial maps      17
Cokernel      12 41 252
Commutation rule for signs      164
Commutative coalgebra      179
Commutative DGA-algebra      312
Commutative diagram      13
Commutator subgroup      290
Comodule      198
Comparison theorem      87 355
Complementary degree      327
Complete semi-simplicial complex      236
COMPLEX      1 39
Complex of complexes      301
Complex over a module      87
Complex under a module      95
Composite extension      65 82
Composite function      9
Composite homomorphism      10 195
Composite morphism      25 249
Composite relation      52
Composite sequence      82
Composition of homomorphism      11 195
Composition principle      53
Condensation      302
Condensed canonical Comparison Theorem      305
Congruence of extensions      64 109 285 368
Congruence of n-fold sequences      83 370
Conjugate module      146
Conjugation      124 131
Conjugation class      124
Connected DG-algebra      192
Connected pair of functors      380
Connected sequence of functors      386
Connecting homomorphism      45 51 96 162
Connecting morphism      380
Connecting relation (for complexes)      333
Connection (cohomology of groups)      347 349
Construction      304
Contractible space      58
Contracting homotopy      41 265 267
Contravariant functor      22 29
Convergence (of spectral sequence)      327 329
Convergent filtration      329
Converse (of a relation)      52
Convex hull      54
Coresolution      95
Correspondence (additive relation)      366
Coset (of a subgroup)      11
Coterminal homomorphisms      16 359
Counit of coalgebra      197
Couniversal      17
Couniversal functor      381 387
Couniversal square      359
Couple, exact      336
Covariant functor      22 28 379 386
Crossed homomorphism      105 284
Crossed product      125
Crossed product extension      125
Cup product      245 394
CYCLE      35 39
Cyclic module      20
Cylinder      59
Degeneracy operator      235
Degree      175
Derived couple      336
Derived functor      389 393
Descending filtration      346
DG-algebra      190
DGA-algebra      192
Diagonal homomorphism      68
Diagonal map      197 244
Diagonal morphism      251
Diagram      33
Diagram chasing      14 364
Differential      35 318
Differential graded algebra      190
Differential graded augmented algebra      192
Differential graded module      189
Differential group      35
Differential module      10
Differential on $Hom_{U}$      191
Differential on Hom(K, L)      43 190
DIMENSION      39
Direct product      27 32
Direct product diagram      27
Direct product of algebras      212 295
Direct product of morphisms      33
Direct sum      15 27
Direct sum diagram      27
Divisible abelian group      93
Domain of definition of relation      52
Domain of function      9
Domain of homomorphism      10
Domain of morphism      25
Dual      27
Dual basis      147
Dual module      146
Dual statement      27
Edge homomorphism      321
Edge homomorphisms      321 335
Eilenberg — Zilber theorem      239 241
Elementary special complex      42
Endomorphism      10 143
Enough projectives      261 367 377
Envelope, injective      103
Enveloping algebra      317
EPIC      252
Epimorphism      10 251
EQUIVALENCE      25 252
Equivalence principle      53
Equivariant cohomology      136
Essential extension      102
Euler characteristic      323
Exact couple      336
Exact functor      263 379
Exact homology sequence      45
Exact sequence      11 256
Exact triangle      193 336
Excision axiom      62
Exterior algebra      174 179 183
External direct sum      15 18
External product      220 221
Face operator      235
Factor set      111 285
Factor system      69
Factorization, standard      254
Factorization, through      12 66 252
Faithful functor      263
Fiber map      322
Fiber terms (of spectral sequence)      321
Fibred product      359
Filtration      165 309 326
Filtration degree      327
Filtration of bar construction      309
Filtration of bicomplex      341
Filtration of tensor product      165
Finite type (module)      20 219
Finitistic dimension      203
First filtration      341
First quadrant spectral sequence      320
Five lemma      14 365
Flat module      163
Forgetful functor      262
Four lemma      14 364
Free complex      87
Free graded module      215
Free group      122 123
Free module      19 195
Free resolution      87
Free ring (over a group)      104
Function      8
functor      28
Generators (of a module)      20
Graded (two-sided) ideal      178
Graded additive category      370
Graded algebra      177
Graded algebras      177
Graded k-module      175
Graded left ideal      178
Graded modules      175
Graded object      177
Graded right ideal      178
Graded set      177
Graded U-module      191
Graph of homomorphism      52
Ground ring extension      213 294
Group algebra      199 295
Group extension      108
Group ring      104
Gysin sequence      326
Half exact functor      379
Hilbert syzygy theorem      217
Hochschild (co)homology modules      283 288
Holomorph of a group      105
Hom-$\bigotimes$ interchange      195
Homogeneous elements      177
Homogeneous generator      119
Homogeneous ideal      180
Homogeneous ideals      178
Homological dimension      201
Homologous cycles      35 40
Homology      35
Homology classes      35 39
Homology group      35 57
Homology isomorphism      310
Homology modules      39
Homology product      166 221 296
Homomorphism      10
Homomorphism of $\Lambda$-modules      184
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