Higher Topos Theory

Abstract

This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the study of higher versions of Grothendieck topoi. A few applications to classical topology are included.

735 pages. An updated and expanded version of the earlier submission math.CT/0306109 2/10/07: Various minor additions and corrections; added some material on combinatorial model categories to the appendix. 3/8/7: Actually uploaded the update this time; added material on fiber products of higher topoi. 7/31/08: Several sections added, others rewritten

Cited by in corpus (14)

• On the Classification of Topological Field Theories
• Derived Algebraic Geometry V: Structured Spaces
• Units of ring spectra and Thom spectra
• On (Enriched) Left Bousfield Localization of Model Categories
• Stable Infinity Categories
• Geometric Cobordism Categories
• Derived Algebraic Geometry IV: Deformation Theory
• Loop Spaces and Langlands Parameters
• Higher-dimensional models of networks
• Periodizable motivic ring spectra
• Topological modular forms (aftern Hopkins, Miller, and Lurie)
• Slices of motivic Landweber spectra
• Differential characters as stacks and prequantization
• Abstract homotopical methods for theoretical computer science