Simplicial methods and the interpretation of "triple" cohomology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
1975
|
| Series: | American Mathematical Society: Memoirs of the American Mathematical Society
163 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 3, Issue 2, Number 163 (first of 2 numbers) |
| Physical Description: | V, 135 S. graph. Darst. |
| ISBN: | 0821818635 |
Staff View
MARC
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| 245 | 1 | 0 | |a Simplicial methods and the interpretation of "triple" cohomology |c J. Duskin |
| 264 | 1 | |a Providence, RI |c 1975 | |
| 300 | |a V, 135 S. |b graph. Darst. | ||
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| 650 | 7 | |a Homologische algebra |2 gtt | |
| 650 | 7 | |a Triple theorie |2 gtt | |
| 650 | 4 | |a Categories (Mathematics) | |
| 650 | 4 | |a Complexes, Semisimplicial | |
| 650 | 4 | |a Homology theory | |
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Record in the Search Index
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|---|---|
| adam_text | TABLE OF CONTENTS
Page
ABSTRACT ii
DEDICATION v
INTRODUCTION l
0. STMPLICIAL OBJECTS IN CATEGORIES 8
0.7 Verdier s Coskeleton Functor 10
0.8 Simplicial Kernels 12
0.11 Augmented Complexes (alternate descriptions) 14
0.12 Contractible and Split Complexes 15
0.13 The Augmented Coskeleton Functor 16
0.14 Stripping or Shift Functor Dec1 18
0.15 The Adjoint Pair ^Dec1) 19
0.17 Nerve of a Category 21
0.19 Homology and Cohomology 25
1. SIMPLICIAL AND COTRIPLE COHOMOLOGY 27
1.1 Cotriple Cohomology 28
1.2 Non Homogeneous Complex 29
1. 3 Triple Cohomology 30
1.4 k Boundary Systems 31 ,
1.5 Differential of a k Boundary System and Cochain Reduction .. 36
2. U SPLIT AUGMENTED COMPLEXES AND THE STANDARD RESOLUTION 39
2.6 k Boundary System Defined by a U Split Complex 44
2.7 Naturality of k Boundary Systems 46
3. HOMOTOPY REPRESENTABILITY OF SIMPLICIAL AND COTRIPLE COHOMOLOGY 49
THE EILENBERG MAC LANE COMPLEXES K(II,n) 49
3.1 Definition of the Complex L(II,n) 50
3.2 Definition of the Complex K(II,n) K n 57
3.7 Corollary (Homotopy Representability of H(X.;I1); 58
3.8 Corollary (Homotopy Representability of %(X;1U ; 58
3.9 Definition of the n th cohomology groupoid M (X.;1O
60
4. K(n,n) TORSORS 72
4.3 Morphisms of n Torsors 74
i:i ^^^^oy^i^or^ ^ r^^^^ 75
n obiects (i.e. Il torsors) above X
5. THE CHARACTERISTIC COCYCLE MAPPING Zn 90
5.3 Functoriality of Z on the Subcategory of Quasi Coherent 92
Morphisms
6. STANDARD K(II,n) T0RS0R DEFINED BY AN n COCYCLE 96
6.1 The Standard Resolution of a T Algebra • • • • • • • • • 98
6.2 Cocycle Formulae 99
6.3 Twisted Product Algebra Defined By a 1 Cocycle 100
6.6.2 Alternative (Quotient) Construction of the Twisted Product
Algebra Defined by a 1 cocycle 103 I ll f] ^
6.7 Construction of the Standard K(Il,n) Torsor Above ^X ^^d 105
by an n cocycle _
6.8 Functoriality of §n(X;II) 108
iii
Page
7. THE INTERPRETATION ADJUNCTIONS Ill
7.2 The Canonical Map Sn(Zn(X.)) » X. 113
7.7 Proof That the Canonical Map f : (Sn(Zn(X.)))n.1 ? (X.)^
Is a Morphism of TT Algebras 118
8. THE INTERPRETATION BIJECTIONS (FIRST CONCLUSIONS) 120
8.9 Theorem (Interpretation of Cotriple Cohomology) 123
APPENDIX. TRIPLES, ALGEBRAS, AND TRIPLEABILITY 125
A.2 Example: Triple Defined by a Pair of Adjoint Functors 125
A.4 The Comparison Functor 126
A.7 Properties 128
A. 8 Inverse Limits 129
A.9 Tripleability Over (ENS) Universal Algebras 129
BIBLIOGRAPHY 132
|
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| indexdate | 2024-07-09T15:53:06Z |
| institution | BVB |
| isbn | 0821818635 |
| language | English |
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| physical | V, 135 S. graph. Darst. |
| publishDate | 1975 |
| publishDateSearch | 1975 |
| publishDateSort | 1975 |
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| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Duskin, John Williford 1937- Verfasser (DE-588)17205799X aut Simplicial methods and the interpretation of "triple" cohomology J. Duskin Providence, RI 1975 V, 135 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 163 Volume 3, Issue 2, Number 163 (first of 2 numbers) Cohomologia larpcal Homologische algebra gtt Triple theorie gtt Categories (Mathematics) Complexes, Semisimplicial Homology theory Triples, Theory of Kohomologie (DE-588)4031700-6 gnd rswk-swf Tripel gnd rswk-swf Tripel f Kohomologie (DE-588)4031700-6 s DE-604 American Mathematical Society: Memoirs of the American Mathematical Society 163 (DE-604)BV008000141 163 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001922858&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Duskin, John Williford 1937- Simplicial methods and the interpretation of "triple" cohomology American Mathematical Society: Memoirs of the American Mathematical Society Cohomologia larpcal Homologische algebra gtt Triple theorie gtt Categories (Mathematics) Complexes, Semisimplicial Homology theory Triples, Theory of Kohomologie (DE-588)4031700-6 gnd |
| subject_GND | (DE-588)4031700-6 |
| title | Simplicial methods and the interpretation of "triple" cohomology |
| title_auth | Simplicial methods and the interpretation of "triple" cohomology |
| title_exact_search | Simplicial methods and the interpretation of "triple" cohomology |
| title_full | Simplicial methods and the interpretation of "triple" cohomology J. Duskin |
| title_fullStr | Simplicial methods and the interpretation of "triple" cohomology J. Duskin |
| title_full_unstemmed | Simplicial methods and the interpretation of "triple" cohomology J. Duskin |
| title_short | Simplicial methods and the interpretation of "triple" cohomology |
| title_sort | simplicial methods and the interpretation of triple cohomology |
| topic | Cohomologia larpcal Homologische algebra gtt Triple theorie gtt Categories (Mathematics) Complexes, Semisimplicial Homology theory Triples, Theory of Kohomologie (DE-588)4031700-6 gnd |
| topic_facet | Cohomologia Homologische algebra Triple theorie Categories (Mathematics) Complexes, Semisimplicial Homology theory Triples, Theory of Kohomologie Tripel |
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| volume_link | (DE-604)BV008000141 |
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