Homotopy theory of higher categories /:
"The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
2012.
|
| Schriftenreihe: | New mathematical monographs ;
19. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others"-- |
| Beschreibung: | 1 online resource (xviii, 634 pages) |
| Bibliographie: | Includes bibliographical references (pages 618-629) and index. |
| ISBN: | 9781139190220 1139190229 9780511978111 0511978111 9781139185325 1139185322 1139188917 9781139188913 9786613378408 6613378402 1139187635 9781139187633 1139183001 9781139183000 |
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| 245 | 1 | 0 | |a Homotopy theory of higher categories / |c Carlos Simpson. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 2012. | ||
| 300 | |a 1 online resource (xviii, 634 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a New mathematical monographs ; |v 19 | |
| 504 | |a Includes bibliographical references (pages 618-629) and index. | ||
| 520 | |a "The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others"-- |c Provided by publisher | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Part I. Higher Categories: 1. History and motivation; 2. Strict n-categories; 3. Fundamental elements of n-categories; 4. Operadic approaches; 5. Simplicial approaches; 6. Weak enrichment over a cartesian model category: an introduction -- Part II. Categorical Preliminaries: 7. Model categories; 8. Cell complexes in locally presentable categories; 9. Direct left Bousfield localization -- Part III. Generators and Relations: 10. Precategories; 11. Algebraic theories in model categories; 12. Weak equivalences; 13. Cofibrations; 14. Calculus of generators and relations; 15. Generators and relations for Segal categories -- Part IV. The Model Structure: 186 Sequentially free precategories; 17. Products; 18. Intervals; 19. The model category of M-enriched precategories -- Part V. Higher Category Theory: 20. Iterated higher categories; 21. Higher categorical techniques; 22. Limits of weak enriched categories; 23. Stabilization. | |
| 546 | |a English. | ||
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| 650 | 0 | |a Categories (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85020992 | |
| 650 | 6 | |a Homotopie. | |
| 650 | 6 | |a Catégories (Mathématiques) | |
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| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
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| 650 | 7 | |a Homotopy theory |2 fast | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn773040607 |
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| _version_ | 1816881783467147264 |
| adam_text | |
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| author | Simpson, Carlos, 1962- |
| author_GND | http://id.loc.gov/authorities/names/n91107507 |
| author_facet | Simpson, Carlos, 1962- |
| author_role | |
| author_sort | Simpson, Carlos, 1962- |
| author_variant | c s cs |
| building | Verbundindex |
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| callnumber-raw | QA612.7 .S56 2012eb |
| callnumber-search | QA612.7 .S56 2012eb |
| callnumber-sort | QA 3612.7 S56 42012EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Part I. Higher Categories: 1. History and motivation; 2. Strict n-categories; 3. Fundamental elements of n-categories; 4. Operadic approaches; 5. Simplicial approaches; 6. Weak enrichment over a cartesian model category: an introduction -- Part II. Categorical Preliminaries: 7. Model categories; 8. Cell complexes in locally presentable categories; 9. Direct left Bousfield localization -- Part III. Generators and Relations: 10. Precategories; 11. Algebraic theories in model categories; 12. Weak equivalences; 13. Cofibrations; 14. Calculus of generators and relations; 15. Generators and relations for Segal categories -- Part IV. The Model Structure: 186 Sequentially free precategories; 17. Products; 18. Intervals; 19. The model category of M-enriched precategories -- Part V. Higher Category Theory: 20. Iterated higher categories; 21. Higher categorical techniques; 22. Limits of weak enriched categories; 23. Stabilization. |
| ctrlnum | (OCoLC)773040607 |
| dewey-full | 512/.62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.62 |
| dewey-search | 512/.62 |
| dewey-sort | 3512 262 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn773040607 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:12Z |
| institution | BVB |
| isbn | 9781139190220 1139190229 9780511978111 0511978111 9781139185325 1139185322 1139188917 9781139188913 9786613378408 6613378402 1139187635 9781139187633 1139183001 9781139183000 |
| language | English |
| oclc_num | 773040607 |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xviii, 634 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
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| publisher | Cambridge University Press, |
| record_format | marc |
| series | New mathematical monographs ; |
| series2 | New mathematical monographs ; |
| spelling | Simpson, Carlos, 1962- https://id.oclc.org/worldcat/entity/E39PBJxCCB6fmdtXQm9V9j4wmd http://id.loc.gov/authorities/names/n91107507 Homotopy theory of higher categories / Carlos Simpson. Cambridge ; New York : Cambridge University Press, 2012. 1 online resource (xviii, 634 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier New mathematical monographs ; 19 Includes bibliographical references (pages 618-629) and index. "The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others"-- Provided by publisher Print version record. Part I. Higher Categories: 1. History and motivation; 2. Strict n-categories; 3. Fundamental elements of n-categories; 4. Operadic approaches; 5. Simplicial approaches; 6. Weak enrichment over a cartesian model category: an introduction -- Part II. Categorical Preliminaries: 7. Model categories; 8. Cell complexes in locally presentable categories; 9. Direct left Bousfield localization -- Part III. Generators and Relations: 10. Precategories; 11. Algebraic theories in model categories; 12. Weak equivalences; 13. Cofibrations; 14. Calculus of generators and relations; 15. Generators and relations for Segal categories -- Part IV. The Model Structure: 186 Sequentially free precategories; 17. Products; 18. Intervals; 19. The model category of M-enriched precategories -- Part V. Higher Category Theory: 20. Iterated higher categories; 21. Higher categorical techniques; 22. Limits of weak enriched categories; 23. Stabilization. English. Homotopy theory. http://id.loc.gov/authorities/subjects/sh85061803 Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Homotopie. Catégories (Mathématiques) MATHEMATICS Topology. bisacsh MATHEMATICS Algebra Intermediate. bisacsh Categories (Mathematics) fast Homotopy theory fast Homotopietheorie gnd http://d-nb.info/gnd/4128142-1 Kategorientheorie gnd http://d-nb.info/gnd/4120552-2 has work: Homotopy theory of higher categories (Text) https://id.oclc.org/worldcat/entity/E39PCGXp3YbwwDWyKKpBvjmBGd https://id.oclc.org/worldcat/ontology/hasWork Print version: Simpson, Carlos, 1962- Homotopy theory of higher categories. Cambridge ; New York : Cambridge University Press, 2012 9780521516952 (DLC) 2011026520 (OCoLC)743431958 New mathematical monographs ; 19. http://id.loc.gov/authorities/names/n2003010567 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=409043 Volltext |
| spellingShingle | Simpson, Carlos, 1962- Homotopy theory of higher categories / New mathematical monographs ; Part I. Higher Categories: 1. History and motivation; 2. Strict n-categories; 3. Fundamental elements of n-categories; 4. Operadic approaches; 5. Simplicial approaches; 6. Weak enrichment over a cartesian model category: an introduction -- Part II. Categorical Preliminaries: 7. Model categories; 8. Cell complexes in locally presentable categories; 9. Direct left Bousfield localization -- Part III. Generators and Relations: 10. Precategories; 11. Algebraic theories in model categories; 12. Weak equivalences; 13. Cofibrations; 14. Calculus of generators and relations; 15. Generators and relations for Segal categories -- Part IV. The Model Structure: 186 Sequentially free precategories; 17. Products; 18. Intervals; 19. The model category of M-enriched precategories -- Part V. Higher Category Theory: 20. Iterated higher categories; 21. Higher categorical techniques; 22. Limits of weak enriched categories; 23. Stabilization. Homotopy theory. http://id.loc.gov/authorities/subjects/sh85061803 Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Homotopie. Catégories (Mathématiques) MATHEMATICS Topology. bisacsh MATHEMATICS Algebra Intermediate. bisacsh Categories (Mathematics) fast Homotopy theory fast Homotopietheorie gnd http://d-nb.info/gnd/4128142-1 Kategorientheorie gnd http://d-nb.info/gnd/4120552-2 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85061803 http://id.loc.gov/authorities/subjects/sh85020992 http://d-nb.info/gnd/4128142-1 http://d-nb.info/gnd/4120552-2 |
| title | Homotopy theory of higher categories / |
| title_auth | Homotopy theory of higher categories / |
| title_exact_search | Homotopy theory of higher categories / |
| title_full | Homotopy theory of higher categories / Carlos Simpson. |
| title_fullStr | Homotopy theory of higher categories / Carlos Simpson. |
| title_full_unstemmed | Homotopy theory of higher categories / Carlos Simpson. |
| title_short | Homotopy theory of higher categories / |
| title_sort | homotopy theory of higher categories |
| topic | Homotopy theory. http://id.loc.gov/authorities/subjects/sh85061803 Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Homotopie. Catégories (Mathématiques) MATHEMATICS Topology. bisacsh MATHEMATICS Algebra Intermediate. bisacsh Categories (Mathematics) fast Homotopy theory fast Homotopietheorie gnd http://d-nb.info/gnd/4128142-1 Kategorientheorie gnd http://d-nb.info/gnd/4120552-2 |
| topic_facet | Homotopy theory. Categories (Mathematics) Homotopie. Catégories (Mathématiques) MATHEMATICS Topology. MATHEMATICS Algebra Intermediate. Homotopy theory Homotopietheorie Kategorientheorie |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=409043 |
| work_keys_str_mv | AT simpsoncarlos homotopytheoryofhighercategories |