LEADER 03900nam 22006373 450 001 996485661003316 005 20221107230448.0 010 $a3-031-10447-1 035 $a(CKB)5850000000052617 035 $a(MiAaPQ)EBC7069232 035 $a(Au-PeEL)EBL7069232 035 $a(OCoLC)on1329425114 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/91316 035 $a(PPN)264191773 035 $a(EXLCZ)995850000000052617 100 $a20220919d2022 fy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSimplicial and dendroidal homotopy theory /$fGijs Heuts, Ieke Moerdijk 210 $aCham$cSpringer Nature$d2022 210 1$aCham :$cSpringer International Publishing AG,$d2022. 210 4$d©2022. 215 $a1 online resource (xx, 612 pages) $cillustrations 225 1 $aErgebnisse der Mathematik und ihrer Grenzgebiete$vv.75 311 $a3-031-10446-3 327 $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 330 $aThis open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with the theory of Quillen model categories. Dendroidal sets are a natural generalization of simplicial sets from the point of view of operads. In this book, the simplicial approach to higher category theory is generalized to a dendroidal approach to higher operad theory. This dendroidal theory of higher operads is carefully developed in this book. The book also provides an original account of the more established simplicial approach to infinity-categories, which is developed in parallel to the dendroidal theory to emphasize the similarities and differences. Simplicial and Dendroidal Homotopy Theory is a complete introduction, carefully written with the beginning researcher in mind and ideally suited for seminars and courses. It can also be used as a standalone introduction to simplicial homotopy theory and to the theory of infinity-categories, or a standalone introduction to the theory of Quillen model categories and Bousfield localization. 410 0$aErgebnisse der Mathematik und ihrer Grenzgebiete$v75. 606 $aHomotopy theory 606 $aTeoria de l'homotopia$2thub 608 $aLlibres electrònics$2thub 610 $aOperads 610 $ainfinity-operad 610 $ainfinity-category 610 $asimplicial set 610 $adendroidal set 610 $asimplicial space 610 $asimplicial operad 610 $amodel categories 610 $aBousfield localization 610 $aBoardman-Vogt 610 $ahigher algebra 615 0$aHomotopy theory. 615 7$aTeoria de l'homotopia 700 $aHeuts$b Gijs$01255141 701 $aMoerdijk$b Ieke$059494 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996485661003316 996 $aSimplicial and dendroidal homotopy theory$92910255 997 $aUNISA