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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
Homomorphism of algebras      177
Homomorphism of bimodules      143
Homomorphism of coalgebras      197
Homomorphism of DG-algebras      190
Homomorphism of differential groups      36
Homomorphism of graded algebras      177
Homomorphism of graded modules      175
Homomorphism of Hopf algebras      198
Homomorphism of modules      10
Homomorphism of spectral sequences      319
Homotopy      39 57
Homotopy classification theorem      78
Hopf algebra      198
Hopf wedge product      231
Hyperhomology groups      400 402
Ideal      10
Identity element      9
Identity function      9 10
Identity morphism      25 249
Image      10 255
Image of morphism      255
Indeterminacy      52
Induced additive relation      53
Induced homomorphism      13 36 255
Induced relation      53
Inessential extension      102
Inflation homomorphism      347
Injection (identity)      9
Injective complex      95
Injective envelope      103
Injective function      251 362
Injective module      92
Injective object (in a category)      261
Injective resolution      95
Inner automorphism      124
Integral group ring      104
Internal direct sum      19
Internal grading      177 180 215
Internal homology product      221
Internal product      221 232
Internally graded algebras      180 215
Internally graded module      177
Internally graded modules      177
Intersection      13 18 364
Invariant boundary      45 61
Invariant element      122 284
Inverse      11 25
Inverse image      13 363
Isomorphism      10
Iterated connecting homomorphism      97
Ker-coker sequence      50
Kernel      10 252 362 363
Koszul resolution      205 218
Kronecker product      182
Krull dimension      220
Kuenneth formula      166
Kuenneth Formula for abelian groups      168
Kuenneth spectral sequence      400
Left $\Lambda$-module      184
Left bar      282
Left derived functor      389
Left equivalence      252
Left exact functor      379
Left exact sequence      23 365
Left global dimension      202
Left injective dimension      203
Left inverse      11
Left module      9
Left R-module      9
Left satellite      382
Left universal pair      381
Leray — Serre Theorem      322
Lie algebra      317
Lifted map      20 87
Lifting functor      301
Line segment      54
Local ring      219
Loop space      325
Lyndon spectral sequence      351 ff. 358
Mapping cone      46 47
Mapping cylinder      46
Mapping function      29 31
Mapping theorem      321
Middle associative      138
Middle associativity      138 186
Middle four interchange      194
Middle linear      138
Minimal resolution      217
Modular Noether isomorphism      318
Module      9
Module extension      63
Monic      251
Monogenic module      20
Monoid      290
Monomorphism      10 251
Monotonic map      233
Monotonic maps      233
Morphism      25 249
Morphism of connected pairs      381
Morphism of exact sequence      63 83
Morphism of extension      63 109
Morphism of group extension      109
Multiplicator      137
n-fold exact sequence      82 83
Natural isomorphism      29
Natural transformation      29 30 32 386
Negative and positive sequence      386
Negative complex      41
Nilpotent ideal      286
Noether isomorphism      13 318
Noether, Emmy      63
Noetherian module      219
Non homogeneous generator      118 119
Norm      110
Normalization      114
Normalization theorem      236 282
Normalized function      281 283
Normalized functor      259
Normalized simplicial complex      236
Null morphism      259
Null object      258
Object      25
Object function      28 31
Obstruction of abstract kernel      126
Obstruction of homomorphisms      72 74
Operator extension      108
Opposite algebra      182
Opposite category      28
Opposite ring      157
Orbit      131
Order (of homotopy)      331
Outer automorphism      124
Outside associativity      187
p-group      132
Pair of spaces      61
Pairing      148 247
Partly ordered set      33 362
Poincare      63
Pointed set      362
Pointed sets      362
Polynomial algebra      179 182
Positive bicomplex      340
Positive complex      41
Positive grading      175
Positively graded modules      175
Preadditive category      250
Prime ideal      218
Principal crossed homomorphism      106 284
PRODUCT      173
Projection of cartesian product      18
Projection on quotient      11
Projective complex      87 261
Projective equivalence      101
Projective module      20
Projective resolution      87
Proper class      367
Proper exact sequence      367 370
Proper ideal      218
Proper long exact sequence      370
Proper morphism      368
Proper open set      134
Proper operators      134
Proper projective object      376
Proper right exact sequence      379
Proper sequence of complexes      397
Proper short exact sequence      367 379
Pull-back      90 143
Pull-back Lemma      140
Pure group extension      367
Pure subgroup      367
Quotient algebra      178
Quotient complex      41
Quotient group      11
Quotient module      11
Quotient object      252 363
Quotient space      134
Range of a function      9
Range of a homomorphism      10
Range of a morphism      25
Reduced bar      283
Reduced bar resolution      283
Reduced module      304
Regular ring      220
Relative abelian category      263
Relative boundary      61
Relative cycle      61
Relative ext functor      269
Relative homology group      61
Relative projective      265 273
Relative projective module      265 273
Relative projective object      265
Relative torsion product      274 275
Relatively free complex      267
Relatively free construction      304
Relatively free module      196
Relatively projective object      265
Residue field (of a local ring)      219
Resolution      87
Resolvent pair (of categories)      265
Restriction homomorphism      347
Right dimension      203
Right equivalence      252
Right equivalent      252
Right exact functor      379
Right exact sequence      23 379
Right module      9 138
Right satellite      384
Ring of endomorphism      21 143
Ring of quotients      219
Ringoid      250
S-split sequence      275
Schematic diagram      263
Second filtration      342
Selective abelian category      256
Selective category      256
Semi-direct product      105
Semi-simple module      203
Semi-simple ring      203
Semidirect product      105
Semidirect sum      286
Separable algebra      214
Sheets of a covering      134
Short exact sequence      12 16
Short Five Lemma      13 256
Short projective resolution      382
Shuffle      243 313
Signature (of a shuffle)      243
Signs (commutation rule)      164
Simple module      203
Simplicial cup product      245
Simplicial diagonal      244
Simplicial map      235
Simplicial module      233
Simplicial object      233
Simplicial sets      233
Singular cohomology group      57
Singular complex      56
Singular extension      284
Skew and anticommutative      178
Small category      26
Special complex      42
Split exact sequence      16 260
Strictly commutative      179
Submodule module      10
Symmetric algebra      184
Tensor algebra      179
Tensor product of graded algebras      181
Total degree      176 318
Total matrix algebra      214
Trigraded module      176
Trivial module      105
Trivially graded module      175
Trivially graded modules      175
Un-normalized bar      115 282
Ungraded algebra      180
Unitary module      9
Weak dimension      203
Weakly split sequence      260
Wedge product      228
Yoneda composite      82
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