國立虎尾科技大學 |

Simplicial and Dendroidal Homotopy Theory

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Simplicial and Dendroidal Homotopy Theory/ by Gijs Heuts, Ieke Moerdijk.
作者:	Heuts, Gijs.
其他作者:	Moerdijk, Ieke.
面頁冊數:	XX, 612 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Algebraic Topology. -
電子資源:	https://doi.org/10.1007/978-3-031-10447-3
ISBN:	9783031104473

Simplicial and Dendroidal Homotopy Theory
Heuts, Gijs.

Simplicial and Dendroidal Homotopy Theory[electronic resource] /by Gijs Heuts, Ieke Moerdijk. - 1st ed. 2022. - XX, 612 p. 1 illus.online resource. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,752197-5655 ;. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,63.

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

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

672209
Algebraic Topology.

LC Class. No.: QA169

Dewey Class. No.: 512.6

Simplicial and Dendroidal Homotopy Theory
LDR:03504nam a22004215i 4500 001 1089288
003 DE-He213
005 20220802120017.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783031104473 $9 978-3-031-10447-3
024 7 $a 10.1007/978-3-031-10447-3 $2 doi
035 $a 978-3-031-10447-3
050 4 $a QA169
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.6 $2 23
100 1 $a Heuts, Gijs. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1396537
245 1 0 $a Simplicial and Dendroidal Homotopy Theory $h [electronic resource] / $c by Gijs Heuts, Ieke Moerdijk.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a XX, 612 p. 1 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, $x 2197-5655 ; $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 0 $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 2 4 $a Algebraic Topology. $3 672209
650 1 4 $a Category Theory, Homological Algebra. $3 678397
650 0 $a Algebraic topology. $3 678206
650 0 $a Algebra, Homological. $3 672614
700 1 $a Moerdijk, Ieke. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1211325
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783031104466
776 0 8 $i Printed edition: $z 9783031104480
830 0 $a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, $x 0071-1136 ; $v 63 $3 1267908
856 4 0 $u https://doi.org/10.1007/978-3-031-10447-3
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
912 $a ZDB-2-SOB
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)