#
nLab

homotopy theory of Grothendieck

## Idea

Alexander Grothendieck outlined, in Pursuing Stacks and Les Derivateurs, a systematic approach to homotopy theory using small categories and basic localizers, and categories of presheaves on a small category, as models for homotopy types. An example of the latter is the category of simplicial sets, which are presheaves on the simplex category $\Delta$.

This approach has been continued in the past decade, mostly by Georges Maltsiniotis and Denis-Charles Cisinski.

### References

G. Maltsiniotis, *La théorie de l’homotopie de Grothendieck*, Astérisque, 301, pp. 1-140, (2005).

Revised on May 29, 2010 05:40:13
by

Mike Shulman
(75.3.130.212)