Simplicial and Dendroidal Homotopy Theory
This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with th...
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| Główni autorzy: | , |
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| Format: | Online |
| Język: | angielski |
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Springer Nature
2022
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| Hasła przedmiotowe: | |
| Dostęp online: | ONIX_20220817_9783031104473_3 |
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| _version_ | 1869518314232872960 |
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| author | Heuts, Gijs Moerdijk, Ieke |
| author_browse | Heuts, Gijs Moerdijk, Ieke |
| author_facet | Heuts, Gijs Moerdijk, Ieke |
| author_sort | Heuts, Gijs |
| collection | Directory of Open Access Books |
| description | This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with the theory of Quillen model categories. Dendroidal sets are a natural generalization of simplicial sets from the point of view of operads. In this book, the simplicial approach to higher category theory is generalized to a dendroidal approach to higher operad theory. This dendroidal theory of higher operads is carefully developed in this book. The book also provides an original account of the more established simplicial approach to infinity-categories, which is developed in parallel to the dendroidal theory to emphasize the similarities and differences. Simplicial and Dendroidal Homotopy Theory is a complete introduction, carefully written with the beginning researcher in mind and ideally suited for seminars and courses. It can also be used as a standalone introduction to simplicial homotopy theory and to the theory of infinity-categories, or a standalone introduction to the theory of Quillen model categories and Bousfield localization. |
| format | Online |
| id | doab-20.500.12854ir-91316 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | Springer Nature |
| publisherStr | Springer Nature |
| record_format | ojs |
| spelling | doab-20.500.12854ir-913162025-05-09T10:56:05Z Simplicial and Dendroidal Homotopy Theory Heuts, Gijs Moerdijk, Ieke Operads infinity-operad infinity-category simplicial set dendroidal set simplicial space simplicial operad model categories Bousfield localization Boardman-Vogt higher algebra This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with the theory of Quillen model categories. Dendroidal sets are a natural generalization of simplicial sets from the point of view of operads. In this book, the simplicial approach to higher category theory is generalized to a dendroidal approach to higher operad theory. This dendroidal theory of higher operads is carefully developed in this book. The book also provides an original account of the more established simplicial approach to infinity-categories, which is developed in parallel to the dendroidal theory to emphasize the similarities and differences. Simplicial and Dendroidal Homotopy Theory is a complete introduction, carefully written with the beginning researcher in mind and ideally suited for seminars and courses. It can also be used as a standalone introduction to simplicial homotopy theory and to the theory of infinity-categories, or a standalone introduction to the theory of Quillen model categories and Bousfield localization. 2022-08-18T04:03:51Z 2022-08-18T04:03:51Z 2022-08-17T20:13:43Z 2022 book ONIX_20220817_9783031104473_3 ONIX_20220817_9783031104473_3 OCN: 1340410536 https://library.oapen.org/handle/20.500.12657/57895 9783031104473 https://directory.doabooks.org/handle/20.500.12854/91316 eng Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics open access image/jpeg image/jpeg image/jpeg image/jpeg image/jpeg n/a n/a n/a n/a n/a https://library.oapen.org/bitstream/20.500.12657/57895/1/978-3-031-10447-3.pdf https://library.oapen.org/bitstream/20.500.12657/57895/1/978-3-031-10447-3.pdf https://library.oapen.org/bitstream/20.500.12657/57895/1/978-3-031-10447-3.pdf https://library.oapen.org/bitstream/20.500.12657/57895/1/978-3-031-10447-3.pdf https://library.oapen.org/bitstream/20.500.12657/57895/1/978-3-031-10447-3.pdf Springer Nature Springer 10.1007/978-3-031-10447-3 10.1007/978-3-031-10447-3 9fa3421d-f917-4153-b9ab-fc337c396b5a Nederlandse Organisatie voor Wetenschappelijk Onderzoek H2020 European Research Council da087c60-8432-4f58-b2dd-747fc1a60025 9783031104473 Dutch Research Council (NWO) European Research Council (ERC) EU collection Springer 612 Cham 016-VENI-192-186 950048 open access |
| spellingShingle | Operads infinity-operad infinity-category simplicial set dendroidal set simplicial space simplicial operad model categories Bousfield localization Boardman-Vogt higher algebra Heuts, Gijs Moerdijk, Ieke Simplicial and Dendroidal Homotopy Theory |
| title | Simplicial and Dendroidal Homotopy Theory |
| title_full | Simplicial and Dendroidal Homotopy Theory |
| title_fullStr | Simplicial and Dendroidal Homotopy Theory |
| title_full_unstemmed | Simplicial and Dendroidal Homotopy Theory |
| title_short | Simplicial and Dendroidal Homotopy Theory |
| title_sort | simplicial and dendroidal homotopy theory |
| topic | Operads infinity-operad infinity-category simplicial set dendroidal set simplicial space simplicial operad model categories Bousfield localization Boardman-Vogt higher algebra |
| topic_facet | Operads infinity-operad infinity-category simplicial set dendroidal set simplicial space simplicial operad model categories Bousfield localization Boardman-Vogt higher algebra |
| url | ONIX_20220817_9783031104473_3 |
| work_keys_str_mv | AT heutsgijs simplicialanddendroidalhomotopytheory AT moerdijkieke simplicialanddendroidalhomotopytheory |