rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Simplicial and Dendroidal Homotopy Theory
  name:
    name part: Heuts, Gijs.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Moerdijk, Ieke.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: sz
    date issued: 2022
    edition: 1st ed. 2022.
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (XX, 612 pages 1 illustrations)
  abstract: 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.
  table of contents: 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.
  note: by Gijs Heuts, Ieke Moerdijk.
  note: Open Access
  subject:
    topic: Algebra, Homological
  subject:
    topic: Algebraic topology
  subject:
    topic: Category Theory, Homological Algebra
  subject:
    topic: Algebraic Topology
  classification: QA169
  classification: 512.6
  related item:
    title info:
      title: Springer Nature eBook
  related item:
    title info:
      title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 75
  identifier: 9978-3-031-10447-3
  identifier: 9783031104473
  identifier: https://doi.org/10.1007/978-3-031-10447-3
  access condition: Open Access
  record info:
    record creation date: 220802
    record change date: 20230829020326.7
    record identifier: in00004662137