Simplicial and dendroidal homotopy theory / Gijs Heuts, Ieke Moerdijk.
Heuts, Gijs, author.; Moerdijk, Ieke, author.
2022
QA612.7
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Title Simplicial and dendroidal homotopy theory / Gijs Heuts, Ieke Moerdijk.
Author Heuts, Gijs, author.
ISBN 9783031104473 (electronic bk.)
3031104471 (electronic bk.)
9783031104466 (print)
DOI https://doi.org/10.1007/978-3-031-10447-3
Published Cham, Switzerland : Springer, 2022.
Language English
Description 1 online resource (xx, 612 pages) : illustrations.
Item Number 10.1007/978-3-031-10447-3 doi
Call Number QA612.7
Dewey Decimal Classification 514/.24
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Open access.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed August 10, 2022).
Added Author Moerdijk, Ieke, author.
Series Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 75. 2197-5655
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Part 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.

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