Simplicial and Dendroidal Homotopy Theory

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Both authors are experienced researchers in the field who have contributed significantly to the development of the theory contained in this book. They have lectured extensively on simplicial and dendroidal sets.

Zusammenfassung

The first book developing the homotopy theory of infinity-operads

Provides a self-contained introduction to the theory of simplicial sets and infinity-categories

Includes complete proofs of all the basic results, with special attention paid to the underlying combinatorics

This book is open access, which means that you have free and unlimited access

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2022
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Inhalt:	xx 612 S. 1 s/w Illustr. 612 p. 1 illus.
ISBN-13:	9783031104466
ISBN-10:	3031104463
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Moerdijk, Ieke Heuts, Gijs
Auflage:	1st ed. 2022
Hersteller:	Springer International Publishing Springer International Publishing AG Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Maße:	241 x 160 x 40 mm
Von/Mit:	Ieke Moerdijk (u. a.)
Erscheinungsdatum:	03.08.2022
Gewicht:	1,103 kg

Artikel-ID: 121975964