nLab
Homotopy Theory of Higher Categories

higher category theory

Basic concepts

Basic theorems

Applications

Models

(n,r)-category
- Theta-space
- ∞-category/ω-category
- (∞,n)-category
  - n-fold complete Segal space
- (∞,2)-category
- (∞,1)-category
- (∞,0)-category/∞-groupoid
  - Kan complex
    - algebraic Kan complex
    - simplicial T-complex
- n-category = (n,n)-category
- n-poset = (n-1,n)-category
  - poset = (0,1)-category
  - 2-poset = (1,2)-category
- n-groupoid = (n,0)-category
  - 2-groupoid, 3-groupoid
categorification/decategorification
geometric definition of higher category
algebraic definition of higher category
stable homotopy theory

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

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Carlos Simpson, Homotopy Theory of Higher Categories, draft of a book http://arxiv.org/abs/1001.4071 (alternative URL with hyperTeX-ed crosslinks: pdf)

on higher category theory.

category: reference

Revised on October 26, 2010 05:07:07 by Toby Bartels (75.117.105.71)