Pursuing Stacks

Pursuing Stacks (French: À la Poursuite des Champs) is an influential 1983 mathematical manuscript by Alexander Grothendieck. The word "stack" refers to a possible generalization of scheme, a central object of study in algebraic geometry.

Among the concepts introduced in the manuscript are derivators and test categories.

Some parts of the manuscript were later developed in:

• Georges Maltsiniotis (2005), "La théorie de l'homotopie de Grothendieck" [Grothendieck's homotopy theory] (PDF), Astérisque, 301, MR 2200690
• Denis-Charles Cisinski (2006), "Les préfaisceaux comme modèles des types d'homotopie" [Presheaves as models for homotopy types] (PDF), Astérisque, 308, ISBN 978-2-85629-225-9, MR 2294028

See also

• Homotopy hypothesis

References

• Is there a high-concept explanation for why “simplicial” leads to “homotopy-theoretic”?
• What's special about the Simplex category?
• R. Brown, The Origins of `Pursuing Stacks' by Alexander Grothendieck

External links

• http://ncatlab.org/nlab/show/Pursuing+Stacks
• Conjectures in Grothendieck's “Pursuing stacks”