Categorical homotopy theory:
This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admi...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2014
|
| Schriftenreihe: | New mathematical monographs
24 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UER01 Volltext |
| Zusammenfassung: | This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xviii, 352 pages) |
| ISBN: | 9781107261457 |
| DOI: | 10.1017/CBO9781107261457 |
Internformat
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| 520 | |a This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence | ||
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Datensatz im Suchindex
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| author | Riehl, Emily 1983- |
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| author_facet | Riehl, Emily 1983- |
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| author_sort | Riehl, Emily 1983- |
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| dewey-full | 514/.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| dewey-search | 514/.24 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781107261457 |
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| id | DE-604.BV043942089 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9781107261457 |
| language | English |
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| oclc_num | 967776290 |
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| owner_facet | DE-12 DE-29 DE-92 |
| physical | 1 online resource (xviii, 352 pages) |
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| publishDate | 2014 |
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| publisher | Cambridge University Press |
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| series | New mathematical monographs |
| series2 | New mathematical monographs |
| spelling | Riehl, Emily 1983- Verfasser (DE-588)1058749897 aut Categorical homotopy theory Emily Riehl, Harvard University Cambridge Cambridge University Press 2014 1 online resource (xviii, 352 pages) txt rdacontent c rdamedia cr rdacarrier New mathematical monographs 24 Title from publisher's bibliographic system (viewed on 05 Oct 2015) This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence Homotopy theory Algebra, Homological Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Homologische Algebra (DE-588)4160598-6 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 s Kategorientheorie (DE-588)4120552-2 s Homologische Algebra (DE-588)4160598-6 s 1\p DE-604 Erscheint auch als Druck-Ausgabe, Hardcover 978-1-107-04845-4 New mathematical monographs 24 (DE-604)BV045080773 24 https://doi.org/10.1017/CBO9781107261457 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Riehl, Emily 1983- Categorical homotopy theory New mathematical monographs Homotopy theory Algebra, Homological Kategorientheorie (DE-588)4120552-2 gnd Homotopietheorie (DE-588)4128142-1 gnd Homologische Algebra (DE-588)4160598-6 gnd |
| subject_GND | (DE-588)4120552-2 (DE-588)4128142-1 (DE-588)4160598-6 |
| title | Categorical homotopy theory |
| title_auth | Categorical homotopy theory |
| title_exact_search | Categorical homotopy theory |
| title_full | Categorical homotopy theory Emily Riehl, Harvard University |
| title_fullStr | Categorical homotopy theory Emily Riehl, Harvard University |
| title_full_unstemmed | Categorical homotopy theory Emily Riehl, Harvard University |
| title_short | Categorical homotopy theory |
| title_sort | categorical homotopy theory |
| topic | Homotopy theory Algebra, Homological Kategorientheorie (DE-588)4120552-2 gnd Homotopietheorie (DE-588)4128142-1 gnd Homologische Algebra (DE-588)4160598-6 gnd |
| topic_facet | Homotopy theory Algebra, Homological Kategorientheorie Homotopietheorie Homologische Algebra |
| url | https://doi.org/10.1017/CBO9781107261457 |
| volume_link | (DE-604)BV045080773 |
| work_keys_str_mv | AT riehlemily categoricalhomotopytheory |