Higher Topos Theory
Category Theory
2008-07-31 v4 Algebraic Topology
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.
Cite
@article{arxiv.math/0608040,
title = {Higher Topos Theory},
author = {Jacob Lurie},
journal= {arXiv preprint arXiv:math/0608040},
year = {2008}
}
Comments
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