nLab
Homotopy Theory of Higher Categories

higher category theory

Definitions

(n,r)-category
- Theta-space
- ∞-category/ω-category
- (∞,n)-category
  - n-fold complete Segal space
- (∞,2)-category
- (∞,1)-category
- (∞,0)-category/∞-groupoid
  - Kan complex
- n-category = (n,n)-category
- n-poset = (n−1,n)-category
- n-groupoid = (n,0)-category
- 2-category
- (2,1)-category
- 2-groupoid
- 2-poset
- 1-category
- 0-category
- (-1)-category
- (-2)-category
categorification/decategorification
geometric definition of higher category
algebraic definition of higher category
- bicategory
- tricategory
- tetracategory
- strict ω-category
- Batanin ω-category
- Trimble ω-category
- Grothendieck weak ∞-groupoid?
stable homotopy theory

Universal constructions

Higher topos theory

higher topos theory
- (∞,1)-topos

1-categorical models

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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: references

Revised on January 25, 2010 11:01:19 by Zoran Škoda (161.53.130.104)