000 | 04051nam a22005295i 4500 | ||
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001 | 978-3-031-10447-3 | ||
003 | DE-He213 | ||
005 | 20240508090327.0 | ||
007 | cr nn 008mamaa | ||
008 | 220802s2022 sz | s |||| 0|eng d | ||
020 |
_a9783031104473 _9978-3-031-10447-3 |
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024 | 7 |
_a10.1007/978-3-031-10447-3 _2doi |
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050 | 4 | _aQA169 | |
072 | 7 |
_aPBF _2bicssc |
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072 | 7 |
_aMAT002010 _2bisacsh |
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072 | 7 |
_aPBF _2thema |
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082 | 0 | 4 |
_a512.6 _223 |
100 | 1 |
_aHeuts, Gijs. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aSimplicial and Dendroidal Homotopy Theory _h[electronic resource] / _cby Gijs Heuts, Ieke Moerdijk. |
250 | _a1st ed. 2022. | ||
264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2022. |
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300 |
_aXX, 612 p. 1 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, _x2197-5655 ; _v75 |
|
505 | 0 | _aPart I The Elementary Theory of Simplicial and Dendroidal Sets -- 1 Operads -- 2 Simplicial Sets -- 3 Dendroidal Sets -- 4 Tensor Products of Dendroidal Sets -- 5 Kan Conditions for Simplicial Sets -- 6 Kan Conditions for Dendroidal Sets -- Part II The Homotopy Theory of Simplicial and Dendroidal Sets -- 7 Model Categories -- 8 Model Structures on the Category of Simplicial Sets -- 9 Three Model Structures on the Category of Dendroidal Sets -- Part III The Homotopy Theory of Simplicial and Dendroidal Spaces -- 10 Reedy Categories and Diagrams of Spaces -- 11 Mapping Spaces and Bousfield Localizations -- 12 Dendroidal Spaces and ∞-Operads -- 13 Left Fibrations and the Covariant Model Structure -- 14 Simplicial Operads and ∞-Operads -- Epilogue -- References -- Index. | |
506 | 0 | _aOpen Access | |
520 | _aThis 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. | ||
650 | 0 | _aAlgebra, Homological. | |
650 | 0 | _aAlgebraic topology. | |
650 | 1 | 4 | _aCategory Theory, Homological Algebra. |
650 | 2 | 4 | _aAlgebraic Topology. |
700 | 1 |
_aMoerdijk, Ieke. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer Nature eBook | |
776 | 0 | 8 |
_iPrinted edition: _z9783031104466 |
776 | 0 | 8 |
_iPrinted edition: _z9783031104480 |
830 | 0 |
_aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, _x2197-5655 ; _v75 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-031-10447-3 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-SXMS | ||
912 | _aZDB-2-SOB | ||
999 |
_c37762 _d37762 |