TL;DR
This book introduces higher category theory using quasicategories and explores their application to higher Grothendieck topoi, with some classical topology applications.
Contribution
It provides a comprehensive introduction to higher category theory and extends it to the study of higher Grothendieck topoi, connecting abstract theory with topology.
Findings
Development of the formalism of quasicategories
Application to higher Grothendieck topoi
Classical topology applications
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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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models