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Simplicial and dendroidal homotopy theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Simplicial and dendroidal homotopy theoryby Gijs Heuts, Ieke Moerdijk.
Author:	Heuts, Gijs.
other author:	Moerdijk, Ieke.
Published:	Cham :Springer International Publishing :2022.
Description:	xx, 612 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Homotopy theory.
Online resource:	https://doi.org/10.1007/978-3-031-10447-3
ISBN:	9783031104473$q(electronic bk.)

Simplicial and dendroidal homotopy theory
Heuts, Gijs.

Simplicial and dendroidal homotopy theory[electronic resource] /by Gijs Heuts, Ieke Moerdijk. - Cham :Springer International Publishing :2022. - xx, 612 p. :ill., digital ;24 cm. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,v. 752197-5655 ;. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ;v. 75.

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.

Open access.

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.

ISBN: 9783031104473$q(electronic bk.)

Standard No.: 10.1007/978-3-031-10447-3doiSubjects--Topical Terms:

209299
Homotopy theory.

LC Class. No.: QA612.7 / .H48 2022

Dewey Class. No.: 514.24

Simplicial and dendroidal homotopy theory
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245 1 0 $a Simplicial and dendroidal homotopy theory $h [electronic resource] / $c by Gijs Heuts, Ieke Moerdijk.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xx, 612 p. : $b ill., digital ; $c 24 cm.
490 1 $a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, $x 2197-5655 ; $v v. 75
505 0 $a 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.
506 $a Open access.
520 $a 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.
650 0 $a Homotopy theory. $3 209299
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700 1 $a Moerdijk, Ieke. $3 496954
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830 0 $a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ; $v v. 75 $3 932054
856 4 0 $u https://doi.org/10.1007/978-3-031-10447-3
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