Homology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1994
|
| Ausgabe: | 4. print. |
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
114 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 422 S. graph. Darst. |
| ISBN: | 038703823X 354003823X |
Internformat
MARC
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| 100 | 1 | |a Mac Lane, Saunders |d 1909-2005 |e Verfasser |0 (DE-588)118575953 |4 aut | |
| 245 | 1 | 0 | |a Homology |c Saunders MacLane |
| 250 | |a 4. print. | ||
| 264 | 1 | |a Berlin u.a. |b Springer |c 1994 | |
| 300 | |a X, 422 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v 114 | |
| 650 | 0 | 7 | |a Homologie |0 (DE-588)4141951-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Homologietheorie |0 (DE-588)4141714-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Homologietheorie |0 (DE-588)4141714-8 |D s |
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| 689 | 1 | 0 | |a Homologie |0 (DE-588)4141951-0 |D s |
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Datensatz im Suchindex
| _version_ | 1805066948302602240 |
|---|---|
| adam_text |
TABLE
OF
CONTENTS
PAGE
INTRODUCTION
.
1
CHAPTER
I.
MODULES,
DIAGRAMS,
AND
FUNCTORS
.
8
1.
THE
ARROW
NOTATION
.
8
2.
MODULES
.
9
3.
DIAGRAMS
.
13
4.
DIRECT
SUMS
.
15
5.
FREE
AND
PROJECTIVE
MODULES
.
19
6.
THE
FUNCTOR
HOM
.
21
7.
CATEGORIES
.
25
8.
FUNCTORS
.
28
CHAPTER
II.
HOMOLOGY
OF
COMPLEXES
.
34
1.
DIFFERENTIAL
GROUPS
.
35
2.
COMPLEXES
.
39
3.
COHOMOLOGY
.
42
4.
THE
EXACT
HOMOLOGY
SEQUENCE
.
44
5.
SOME
DIAGRAM
LEMMAS
.
49
6.
ADDITIVE
RELATIONS
.
51
7.
SINGULAR
HOMOLOGY
.
54
8.
HOMOTOPY
.
57
9.
AXIOMS
FOR
HOMOLOGY
.
61
CHAPTER
III.
EXTENSIONS
AND
RESOLUTIONS
.
63
1.
EXTENSIONS
OF
MODULES
.
63
2.
ADDITION
OF
EXTENSIONS
.
67
3.
OBSTRUCTIONS
TO
THE
EXTENSION
OF
HOMOMORPHISMS
.
72
4.
THE
UNIVERSAL
COEFFICIENT
THEOREM
FOR
COHOMOLOGY
.
76
5.
COMPOSITION
OF
EXTENSIONS
.
82
6.
RESOLUTIONS
.
87
7.
INJECTIVE
MODULES
.
92
8.
INJECTIVE
RESOLUTIONS
.
95
9.
TWO
EXACT
SEQUENCES
FOR
EXT
"
.
96
10.
AXIOMATIC
DESCRIPTION
OF
EXT
.
99
11.
THE
INJECTIVE
ENVELOPE
.
102
CHAPTER
IV.
COHOMOLOGY
OF
GROUPS
.
103
1.
THE
GROUP
RING
.
104
2.
CROSSED
HOMOMORPHISMS
.
105
3.
GROUP
EXTENSIONS
.
108
4.
FACTOR
SETS
.
111
5.
THE
BAR
RESOLUTION
.
114
6.
THE
CHARACTERISTIC
CLASS
OF
A
GROUP
EXTENSION
.
120
TABLE
OF
CONTENTS
IX
PAGE
7.
COHOMOLOGY
OF
CYCLIC
AND
FREE
GROUPS
.
121
8.
OBSTRUCTIONS
TO
EXTENSIONS
.
124
9.
REALIZATION
OF
OBSTRUCTIONS
.
129
10.
S
CHUR
'
S
THEOREM
.
131
11.
SPACES
WITH
OPERATORS
.
134
CHAPTER
V.
TENSOR
AND
TORSION
PRODUCTS
.
138
1.
TENSOR
PRODUCTS
.
138
2.
MODULES
OVER
COMMUTATIVE
RINGS
.
141
3.
BIMODULES
.
142
4.
DUAL
MODULES
.
146
5.
RIGHT
EXACTNESS
OF
TENSOR
PRODUCTS
.
148
6.
TORSION
PRODUCTS
OF
GROUPS
.
150
7.
TORSION
PRODUCTS
OF
MODULES
.
154
8.
TORSION
PRODUCTS
BY
RESOLUTIONS
.
159
9.
THE
TENSOR
PRODUCT
OF
COMPLEXES
.
163
10.
THE
KO
NNETH
FORMULA
.
166
11.
UNIVERSAL
COEFFICIENT
THEOREMS
.
170
CHAPTER
VI.
TYPES
OF
ALGEBRAS
.
173
1.
ALGEBRAS
BY
DIAGRAMS
.
173
2.
GRADED
MODULES
.
175
3.
GRADED
ALGEBRAS
.
177
4.
TENSOR
PRODUCTS
OF
ALGEBRAS
.
181
5.
MODULES
OVER
ALGEBRAS
.
184
6.
COHOMOLOGY
OF
FREE
ABELIAN
GROUPS
.
187
7.
DIFFERENTIAL
GRADED
ALGEBRAS
.
189
8.
IDENTITIES
ON
HOM
AND
193
9.
COALGEBRAS
AND
H
OPF
ALGEBRAS
.
197
CHAPTER
VII.
DIMENSION
.
200
1.
HOMOLOGICAL
DIMENSION
.
200
2.
DIMENSIONS
IN
POLYNOMIAL
RINGS
.
204
3.
EXT
AND
TOR
FOR
ALGEBRAS
.
206
4.
GLOBAL
DIMENSIONS
OF
POLYNOMIAL
RINGS
.
210
5.
SEPARABLE
ALGEBRAS
.
211
6.
GRADED
SYZYGIES
.
215
7.
LOCAL
RINGS
.
218
CHAPTER
VIII.
PRODUCTS
.
220
1.
HOMOLOGY
PRODUCTS
.
220
2.
THE
TORSION
PRODUCT
OF
ALGEBRAS
.
224
3.
A
DIAGRAM
LEMMA
.
227
4.
EXTERNAL
PRODUCTS
FOR
EXT
.
228
5.
SIMPLICIAL
OBJECTS
.
233
6.
NORMALIZATION
.
236
7.
ACYCLIC
MODELS
.
237
8.
THE
E
ILENBERG
-Z
ILBER
THEOREM
.
238
9.
CUP
PRODUCTS
.
244
CHAPTER
IX.
RELATIVE
HOMOLOGICAL
ALGEBRA
.
248
1.
ADDITIVE
CATEGORIES
.
249
2.
ABELIAN
CATEGORIES
.
254
X
TABLE
OF
CONTENTS
PAGE
3.
CATEGORIES
OF
DIAGRAMS
.
257
4.
COMPARISON
OF
ALLOWABLE
RESOLUTIONS
.260
5.
RELATIVE
ABELIAN
CATEGORIES
.262
6.
RELATIVE
RESOLUTIONS
.
265
7.
THE
CATEGORICAL
BAR
RESOLUTION
.270
8.
RELATIVE
TORSION
PRODUCTS
.
273
9.
DIRECT
PRODUCTS
OF
RINGS
.278
CHAPTER
X.
COHOMOLOGY
OF
ALGEBRAIC
SYSTEMS
.280
1.
INTRODUCTION
.
280
2.
THE
BAR
RESOLUTION
FOR
ALGEBRAS
.280
3.
THE
COHOMOLOGY
OF
AN
ALGEBRA
.
283
4.
THE
HOMOLOGY
OF
AN
ALGEBRA
.288
5.
HOMOLOGY
OF
GROUPS
AND
MONOIDS
.290
6.
GROUND
RING
EXTENSIONS
AND
DIRECT
PRODUCTS
.
293
7.
HOMOLOGY
OF
TENSOR
PRODUCTS
.
295
8.
THE
CASE
OF
GRADED
ALGEBRAS
.298
9.
COMPLEXES
OF
COMPLEXES
.
301
10.
RESOLUTIONS
AND
CONSTRUCTIONS
.
303
11.
TWO-STAGE
COHOMOLOGY
OF
DGA-ALGEBRAS
.308
12.
COHOMOLOGY
OF
COMMUTATIVE
DGA-ALGEBRAS
.
311
13.
HOMOLOGY
OF
ALGEBRAIC
SYSTEMS
.
315
CHAPTER
XI.
SPECTRAL
SEQUENCES
.
318
1.
SPECTRAL
SEQUENCES
.
318
2.
FIBER
SPACES
.322
3.
FILTERED
MODULES
.
326
4.
TRANSGRESSION
.
332
5.
EXACT
COUPLES
.
336
6.
BICOMPLEXES
.
340
7.
THE
SPECTRAL
SEQUENCE
OF
A
COVERING
.
342
8.
COHOMOLOGY
SPECTRAL
SEQUENCES
.
345
9.
RESTRICTION,
INFLATION,
AND
CONNECTION
.
345
10.
THE
LYNDON
SPECTRAL
SEQUENCE
.
351
11.
THE
COMPARISON
THEOREM
.
357
CHAPTER
XII.
DERIVED
FUNCTORS
.
358
1.
SQUARES
.
359
2.
SUBOBJECTS
AND
QUOTIENT
OBJECTS
.
361
3.
DIAGRAM
CHASING
.
364
4.
PROPER
EXACT
SEQUENCES
.
367
5.
EXT
WITHOUT
PROJECTIVES
.
371
6.
THE
CATEGORY
OF
SHORT
EXACT
SEQUENCES
.
375
7.
CONNECTED
PAIRS
OF
ADDITIVE
FUNCTORS
.
379
8.
CONNECTED
SEQUENCES
OF
FUNCTORS
.
386
9.
DERIVED
FUNCTORS
.
389
10.
PRODUCTS
BY
UNIVERSALITY
.
394
11.
PROPER
PROJECTIVE
COMPLEXES
.
397
12.
THE
SPECTRAL
KO
NNETH
FORMULA
.400
BIBLIOGRAPHY
.
404
LIST
OF
STANDARD
SYMBOLS
.
413
INDEX
.
415 |
| any_adam_object | 1 |
| author | Mac Lane, Saunders 1909-2005 |
| author_GND | (DE-588)118575953 |
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| id | DE-604.BV009252539 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T03:26:27Z |
| institution | BVB |
| isbn | 038703823X 354003823X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006157770 |
| oclc_num | 75407391 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR DE-634 |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-634 |
| physical | X, 422 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Mac Lane, Saunders 1909-2005 Verfasser (DE-588)118575953 aut Homology Saunders MacLane 4. print. Berlin u.a. Springer 1994 X, 422 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 114 Homologie (DE-588)4141951-0 gnd rswk-swf Homologietheorie (DE-588)4141714-8 gnd rswk-swf Homologie (DE-588)4141951-0 s Homologietheorie (DE-588)4141714-8 s 1\p DE-604 DE-604 Grundlehren der mathematischen Wissenschaften 114 (DE-604)BV000000395 114 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006157770&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mac Lane, Saunders 1909-2005 Homology Grundlehren der mathematischen Wissenschaften Homologie (DE-588)4141951-0 gnd Homologietheorie (DE-588)4141714-8 gnd |
| subject_GND | (DE-588)4141951-0 (DE-588)4141714-8 |
| title | Homology |
| title_auth | Homology |
| title_exact_search | Homology |
| title_full | Homology Saunders MacLane |
| title_fullStr | Homology Saunders MacLane |
| title_full_unstemmed | Homology Saunders MacLane |
| title_short | Homology |
| title_sort | homology |
| topic | Homologie (DE-588)4141951-0 gnd Homologietheorie (DE-588)4141714-8 gnd |
| topic_facet | Homologie Homologietheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006157770&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT maclanesaunders homology |