Description 
1 online resource (v, 120 pages) 
Series 
Memoirs of the American Mathematical Society ; number 1282 

Memoirs of the American Mathematical Society ; no. 1282

Contents 
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 epimono factorization system  2.2. Grothendieck topologies  2.3. Sheaves on ıcategories of ıtopoi.  2.4. The (ı,2)category of ıtopoi.  Chapter 3. Local Homeomorphisms and Étale Maps of ıTopoi  3.1. Topoi as Generalized Spaces  3.2. Local homeomorphisms, sheaves, and étale maps  3.3. The étale topology on ıtopoi 

Chapter 4. Structured ıTopoi  4.1. Structure Sheaves and Classifying Topoi  4.2. Geometries and Geometric Structures  4.3. Étale Morphisms of Structured ıTopoi  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. DeligneMumford Stacks for a Geometry  Bibliography  Back Cover 
Summary 
The author develops a universal framework to study smooth higher orbifolds on the one hand and higher DeligneMumford 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 points of such objects. He chooses to model higher orbifolds and DeligneMumford stacks as infinitytopoi equipped with a structure sheaf, thus naturally generalizing the work of Lurie, but his approach applies not only to different settings of algebraic geometry such as classical algebraic geometry, 
Notes 
"March 2020, volume 264, number 1282 (fifth of 6 numbers)." 
Bibliography 
Includes bibliographical references 
Subject 
Categories (Mathematics)


Orbifolds.


Toposes.


Algebraic geometry  Families, fibrations  Stacks and moduli problems.


Categories (Mathematics)


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.


Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15}  General theory of differentiable manifolds [See also 32Cxx]


Orbifolds


Toposes

Form 
Electronic book

ISBN 
1470458101 

9781470458102 
