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.Comment: 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 rewritte
