nLab homotopy theory of Grothendieck


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 Δ\Delta.

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


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

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