Higher Topos Theory

2006/08/02 by Lurie, Jacob · 63 citations
#18B25 (Secondary #18G30 (Secondary) #55U40 (Primary) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0608040

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.

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Related

• Sites and Grothendieck toposes: an introduction
• Higher Operads, Higher Categories
• Foundations of a Recent Extension of Category Theory and Topos Theory
• A Theory of Elementary Higher Toposes
• A Very Short Introduction to Topos Theory (adapted from Prof. Pettigrew's notes)