Feynman categories:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Paris
Société mathématique de France
2017
|
| Series: | Astérisque
numéro 387 |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seite [155]-161. - Zusammenfassung in englischer und französischer Sprache |
| Physical Description: | vii, 161 Seiten Diagramme |
| ISBN: | 9782856298527 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Titel: Feynman categories
Autor: Kaufmann, Ralph M
Jahr: 2017
FEYNMAN CATEGORIES Ralph M. KAUFMANN k Benjamin C. WARD
CONTENTS Introduction ................................................................ 1 0.1. General overview and background ................................... 1 0.2. Main definition ...................................................... 3 0.3. Examples ........................................................... 4 0.4. Discussion of the results ............................................ 7 0.5. Organization of the text ............................................ 16 Acknowledgments ........................................................ 19 Conventions and notations ............................................... 19 1. Feynman categories ...................................................... 21 1.1. Feynman categories—the definition ................................. 21 1.2. (Re)-Construction ................................................... 22 1.3. Surjections: A simple, but not too simple, example j? sur j ............ 23 1.4. Induced structures .................................................. 24 1.5. Functors as a generalization of operads and S-modules: Ops and G)v(mk 26 1.6. Morphisms of Feynman categories .................................. 29 1.7. Other relevant notions .............................................. 31 1.8. Weaker, alternative and Cartesian enriched notions of Feynman categories .......................................................... 32 1.9. Weak Feynman categories and indexed enriched Feynman categories 36 1.10. Connection to Feynman graphs and physics ........................ 38 1.11. Discussion and relation to other structures ......................... 38 2. Examples ................................................................ 41 2.1. The Feynman category 0 = () and categories indexed over it .................................................................. 42 2.2. Feynman categories indexed over 0 dlr ............................... 45 2.3. Feynman categories indexed over
0 ................................. 49 2.4. More functors ....................................................... 51 2.5. Colored versions .................................................... 51 2.6. Planar versions ...................................................... 51 2.7. Not so classical examples ........................................... 53 2.8. Ops with special elements: units and multiplication .................. 55 2.9. Truncation, stability, and the role of 0,1,2 flag corollas ............. 56 SOCIÉTÉ MATHÉMATIQUE DE FRANCE 2017
CONTENTS vi 2.10. Feynman categories with trivial ‘V ................................. 58 2.11. Remarks on relations to similar notions ............................ 59 3. General constructions .................................................... 61 3.1. Free monoidal construction ..................................... 61 3.2. NC-construction .................................................... 61 3.3. ¡¿fd ec o- Decorated Feynman categories ............................... 63 3.4. Iterating Feynman categories ....................................... 66 3.5. Arrow category ..................................................... 68 3.6. Feynman level category ......................................... 68 3.7. Feynman hyper category S^p ....................................... 70 4. Indexed Enriched Feynman categories, (odd) twists and Hopf algebras .... 73 4.1. Enrichment functors ................................................ 73 4.2. Indexed Feynman ¿^Categories: Orientations and Odd Qfvs ........ 77 4.3. Examples ........................................................... 78 4.4. A Connes-Kreimer style bi-algebra/Hopf algebra structure .......... 79 5. Feynman categories given by generators and relations .................... 83 5.1. Structure of © ...................................................... 83 5.2. Odd versions for Feynman categories with ordered presentations ---- 86 6. Universal Operations ..................................................... 91 6.1. Cocompletion and the universal Feynman category ................. 91 6.2. Enriched Versions ................................................... 93 6.3. Cocompletion for Qfus ................................................ 94 6.4. Generators and weak generators .................................... 94 6.5. Feynman categories indexed over 0 ................................. 94 6.6. Gerstenhaber’s construction and its generalizations in terms of Feynman
categories ................................................ 95 6.7. Collecting results .................................................... 97 6.8. Dual construction gf 0 .............................................. 97 6.9. Infinitesimal automorphism group, graph complex and grt .......... 98 6.10. Universal operations in iterated Feynman categories ............... 99 7. Feynman transform, the (co)bar construction and Master Equations ...... 101 7.1. Preliminaries ........................................................ 101 7.2. Graded Feynman categories ......................................... 102 7.3. The differential ..................................................... 104 7.4. The (Co)bar construction and the Feynman transform .............. 106 7.5. A general master equation .......................................... 109 8. Homotopy theory of ¿ 5 -0p-s c ............................................... 113 8.1. Preliminaries ........................................................ 113 8.2. The Model Structure ................................................ 121 ASTF.RISQUK 387
CONTENTS vii 8.3. Quillen adjunctions from morphisms of Feynman categories ......... 127 8.4. Cofibrant objects .................................................... 128 8.5. Homotopy classes of maps and master equations .................... 130 8.6. W Construction ..................................................... 133 A. Graph Glossary ......................................................... 139 A.l. The category of graphs ............................................. 139 A.2. Extra structures .................................................... 141 A.3. Flag killing and leaf operators; insertion operations ................ 145 B. Topological Model Structure ............................................. 147 Bibliography ................................................................ 155 SOCIÉTÉ MATHÉMATIQUE DE FRANCE 2017
|
| any_adam_object | 1 |
| author | Kaufmann, Ralph M. 1969- Ward, Benjamin C. |
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| indexdate | 2024-07-10T07:50:31Z |
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| isbn | 9782856298527 |
| language | English |
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| physical | vii, 161 Seiten Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Société mathématique de France |
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| series | Astérisque |
| series2 | Astérisque |
| spelling | Kaufmann, Ralph M. 1969- Verfasser (DE-588)115673946 aut Feynman categories Ralph M. Kaufmann and Benjamin C. Ward Paris Société mathématique de France 2017 vii, 161 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Astérisque numéro 387 Literaturverzeichnis: Seite [155]-161. - Zusammenfassung in englischer und französischer Sprache Ward, Benjamin C. Verfasser (DE-588)1236160193 aut Astérisque numéro 387 (DE-604)BV002579439 387 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029753659&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaufmann, Ralph M. 1969- Ward, Benjamin C. Feynman categories Astérisque |
| title | Feynman categories |
| title_auth | Feynman categories |
| title_exact_search | Feynman categories |
| title_full | Feynman categories Ralph M. Kaufmann and Benjamin C. Ward |
| title_fullStr | Feynman categories Ralph M. Kaufmann and Benjamin C. Ward |
| title_full_unstemmed | Feynman categories Ralph M. Kaufmann and Benjamin C. Ward |
| title_short | Feynman categories |
| title_sort | feynman categories |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029753659&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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