Simplicial and Dendroidal Homotopy Theory

Simplicial and Dendroidal Homotopy Theory.jpg

Dublin Core

Title

Simplicial and Dendroidal Homotopy Theory

Subject

Mathematical foundations; Algebraic topology

Description

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.

Creator

Heuts, Gijs
Moerdijk, Ieke

Source

https://library.oapen.org/handle/20.500.12657/57895

Publisher

Springer Nature
Publisher website: https://www.springernature.com/gp/products/books

Date

2022

Contributor

Tatik

Rights

http://creativecommons.org/licenses/by/4.0/

Format

PDF

Language

English

Type

Textbooks

Identifier

DOI: 10.1007/978-3-031-10447-3
ISBN: 9783031104473, 9783031104473

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