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001 978-3-031-10447-3
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020 _a9783031104473
_9978-3-031-10447-3
024 7 _a10.1007/978-3-031-10447-3
_2doi
050 4 _aQA169
072 7 _aPBF
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512.6
_223
100 1 _aHeuts, Gijs.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
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.
300 _aXX, 612 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
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