An Overview of Higher Category Theory

• Published in: Higher Topos Theory Vol. 170; pp. 1 - 52
• Main Author: Lurie, Jacob
• Format: Book Chapter
• Language: English
• Published: United States Princeton University Press 06.07.2009
• Subjects: Abstract spaces; Algebraic topology; Applied mathematics; Applied statistics; Category theory; Dimensional analysis; Dimensionality; Equivalence relation; Euclidean geometry; Formal logic; Functors; Geometry; Homotopy theory; Judicial system; Law; Legal motions; Legal objections; Legal proceedings; Logic; Logical topics; Mathematical logic; Mathematical relations; Mathematical set theory; Mathematics; Morphisms; Nerve of a covering; Philosophy; Plane geometry; Pure mathematics; Set theory; Statistical physics; Statistics; Topological spaces; Topological theorems; Topology; Trial court proceedings; Vertices

This chapter is intended as a general introduction to higher category theory. We begin with what we feel is the most intuitive approach to the subject usingtopological categories. This approach is easy to understand but difficult to work with when one wishes to perform even simple categorical constr...