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Simplicial and dendroidal homotopy theory

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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.

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Detail Information

Series Title

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Call Number

514.24 GIJ s

Publisher

Switzerland : Springer Cham., 2022

Collation

XX, 612 p

Language

English

ISBN/ISSN

9783031104473

Classification

NONE

Content Type

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Media Type

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Carrier Type

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Edition

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Subject(s)

Mathematics
Homotopy theory
Dendroidal

Specific Detail Info

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