Complicial sets characterising the simplicial nerves of strict omega-categories:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
2008
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
905 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | "May 2008, volume 193, number 905 (end of volume)." Includes bibliographical references |
| Beschreibung: | XV, 184 S. |
| ISBN: | 9780821841426 |
Internformat
MARC
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| 245 | 1 | 0 | |a Complicial sets characterising the simplicial nerves of strict omega-categories |c Dominic Verity |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2008 | |
| 300 | |a XV, 184 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 905 | |
| 500 | |a "May 2008, volume 193, number 905 (end of volume)." | ||
| 500 | |a Includes bibliographical references | ||
| 650 | 4 | |a Categories (Mathematics) | |
| 650 | 4 | |a Algebraic topology | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface ix
Historical Background ix
Relationships to Other Work xii
Overview and Structure xiii
Chapter 1. Simplicial Operators and Simplicial Sets 1
1. Simplicial Operators 1
2. The Algebraist s A and 2-Categories 3
3. The Algebraist s A and Monoidal Categories 6
4. Simplicial Sets 10
5. Semi-Simplicial Sets 14
6. Analysing Products of Simplicial Sets - the Theory of Shuffles 15
Chapter 2. A Little Categorical Background 21
1. Reflective Full Subcategories 21
2. LFP-Categories and LE-Theories 25
Chapter 3. Double Categories, 2-Categories and n-Categories 33
1. Categories in the Small 33
2. Double Categories 36
3. 2-Categories and Double Categories with Connections 38
4. n-Categories and ^-Categories 43
Chapter 4. An Introduction to the Decalage Construction 47
1. Nerves and Decalage 47
2. Comonad Transformations and Simplicial Reconstruction 49
Chapter 5. Stratifications and Filterings of Simplicial Sets 55
1. Stratified Simplicial Sets 55
2. Superstructures and Filtered Semi-Simplicial Sets 61
Chapter 6. Pre-Complicial Sets 65
1. Introducing Pre-Complicial Sets 65
2. Tensor Products of Pre-Complicial Sets 66
3. Pre-Tensors and Preservation of t-Extensions 71
4. Some Other Preservation Properties 78
5. A Monoidal Biclosed Structure on Pre-Complicial sets 80
6. Superstructures of Pre-Complicial Sets 83
Chapter 7. Complicial Sets 85
1. Introducing Complicial Sets 85
V
vi CONTENTS
2. Glueing Squares and Filling Lemmas 86
3. Tensor Products and Complicial Sets 90
4. Superstructures of Complicial Sets 102
Chapter 8. The Path Category Construction 105
1. The Complicial Category of Prisms 105
2. Path Categories and Superstructures 108
3. A Complicial Double Category with Connections 110
Chapter 9. Complicial Decalage Constructions 115
1. A Decalage Construction on Complicial Sets 115
2. A Path Construction on Complicially Enriched Categories 120
3. A Decalage Construction on Complicially Enriched Categories 125
4. Semi-Simplicial Reconstruction 127
Chapter 10. Street s w-Categorical Nerve Construction 133
1. Parity Complexes 133
2. Collapsers and Stratified Parity Complexes 147
3. w-Categorical Nerve Constructions 150
4. Products of Parity Complexes and the Complicial Tensor 155
5. An Inductive Proof of the Street-Roberts Conjecture 163
Bibliography 173
|
| adam_txt |
Contents
Preface ix
Historical Background ix
Relationships to Other Work xii
Overview and Structure xiii
Chapter 1. Simplicial Operators and Simplicial Sets 1
1. Simplicial Operators 1
2. The Algebraist's A and 2-Categories 3
3. The Algebraist's A and Monoidal Categories 6
4. Simplicial Sets 10
5. Semi-Simplicial Sets 14
6. Analysing Products of Simplicial Sets - the Theory of Shuffles 15
Chapter 2. A Little Categorical Background 21
1. Reflective Full Subcategories 21
2. LFP-Categories and LE-Theories 25
Chapter 3. Double Categories, 2-Categories and n-Categories 33
1. Categories in the Small 33
2. Double Categories 36
3. 2-Categories and Double Categories with Connections 38
4. n-Categories and ^-Categories 43
Chapter 4. An Introduction to the Decalage Construction 47
1. Nerves and Decalage 47
2. Comonad Transformations and Simplicial Reconstruction 49
Chapter 5. Stratifications and Filterings of Simplicial Sets 55
1. Stratified Simplicial Sets 55
2. Superstructures and Filtered Semi-Simplicial Sets 61
Chapter 6. Pre-Complicial Sets 65
1. Introducing Pre-Complicial Sets 65
2. Tensor Products of Pre-Complicial Sets 66
3. Pre-Tensors and Preservation of t-Extensions 71
4. Some Other Preservation Properties 78
5. A Monoidal Biclosed Structure on Pre-Complicial sets 80
6. Superstructures of Pre-Complicial Sets 83
Chapter 7. Complicial Sets 85
1. Introducing Complicial Sets 85
V
vi CONTENTS
2. Glueing Squares and Filling Lemmas 86
3. Tensor Products and Complicial Sets 90
4. Superstructures of Complicial Sets 102
Chapter 8. The Path Category Construction 105
1. The Complicial Category of Prisms 105
2. Path Categories and Superstructures 108
3. A Complicial Double Category with Connections 110
Chapter 9. Complicial Decalage Constructions 115
1. A Decalage Construction on Complicial Sets 115
2. A Path Construction on Complicially Enriched Categories 120
3. A Decalage Construction on Complicially Enriched Categories 125
4. Semi-Simplicial Reconstruction 127
Chapter 10. Street's w-Categorical Nerve Construction 133
1. Parity Complexes 133
2. Collapsers and Stratified Parity Complexes 147
3. w-Categorical Nerve Constructions 150
4. Products of Parity Complexes and the Complicial Tensor 155
5. An Inductive Proof of the Street-Roberts Conjecture 163
Bibliography 173 |
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| institution | BVB |
| isbn | 9780821841426 |
| language | English |
| lccn | 2008060006 |
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| physical | XV, 184 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Verity, Dominic Verfasser aut Complicial sets characterising the simplicial nerves of strict omega-categories Dominic Verity Providence, R.I. American Mathematical Society 2008 XV, 184 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 905 "May 2008, volume 193, number 905 (end of volume)." Includes bibliographical references Categories (Mathematics) Algebraic topology Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 s DE-604 Memoirs of the American Mathematical Society 905 (DE-604)BV008000141 905 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016471778&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Verity, Dominic Complicial sets characterising the simplicial nerves of strict omega-categories Memoirs of the American Mathematical Society Categories (Mathematics) Algebraic topology Kategorientheorie (DE-588)4120552-2 gnd |
| subject_GND | (DE-588)4120552-2 |
| title | Complicial sets characterising the simplicial nerves of strict omega-categories |
| title_auth | Complicial sets characterising the simplicial nerves of strict omega-categories |
| title_exact_search | Complicial sets characterising the simplicial nerves of strict omega-categories |
| title_exact_search_txtP | Complicial sets characterising the simplicial nerves of strict omega-categories |
| title_full | Complicial sets characterising the simplicial nerves of strict omega-categories Dominic Verity |
| title_fullStr | Complicial sets characterising the simplicial nerves of strict omega-categories Dominic Verity |
| title_full_unstemmed | Complicial sets characterising the simplicial nerves of strict omega-categories Dominic Verity |
| title_short | Complicial sets characterising the simplicial nerves of strict omega-categories |
| title_sort | complicial sets characterising the simplicial nerves of strict omega categories |
| topic | Categories (Mathematics) Algebraic topology Kategorientheorie (DE-588)4120552-2 gnd |
| topic_facet | Categories (Mathematics) Algebraic topology Kategorientheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016471778&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT veritydominic complicialsetscharacterisingthesimplicialnervesofstrictomegacategories |