Higher orbifolds and Deligne-Mumford stacks as structured infinity-topoi /

The author develops a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise as the functor of po...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Carchedi, David Joseph (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, RI : American Mathematical Society, [2020]
Colección:Memoirs of the American Mathematical Society ; no. 1282.
Temas:
Toposes.
Categories (Mathematics)
Orbifolds.
Topos (Mathématiques)
Catégories (Mathématiques)
Categorías (Matemáticas)
Topos (Matemáticas)
Orbifolds
Toposes
Category theory; homological algebra {For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for.
Algebraic geometry > Families, fibrations > Stacks and moduli problems.
Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15} > General theory of differentiable manifolds [See also 32Cxx]
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title page
  • Chapter 1. Introduction
  • 1.1. Overview of our approach
  • 1.2. Organization and Main Results
  • 1.3. Conventions and Notations
  • Acknowledgments
  • Chapter 2. Preliminaries on higher topos theory
  • 2.1. The epi-mono factorization system
  • 2.2. Grothendieck topologies
  • 2.3. Sheaves on ı-categories of ı-topoi.
  • 2.4. The (ı,2)-category of ı-topoi.
  • Chapter 3. Local Homeomorphisms and Étale Maps of ı-Topoi
  • 3.1. Topoi as Generalized Spaces
  • 3.2. Local homeomorphisms, sheaves, and étale maps
  • 3.3. The étale topology on ı-topoi.
  • Chapter 4. Structured ı-Topoi
  • 4.1. Structure Sheaves and Classifying Topoi
  • 4.2. Geometries and Geometric Structures
  • 4.3. Étale Morphisms of Structured ı-Topoi
  • Chapter 5. Étendues: Gluing Local Models
  • 5.1. Étendues
  • 5.2. The functor of points approach
  • 5.3. A classification of the functor of points.
  • Chapter 6. Examples
  • 6.1. Higher Differentiable Orbifolds and Étale Stacks
  • 6.2. Deligne-Mumford Stacks for a Geometry
  • Bibliography
  • Back Cover

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