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 by:

• Maltsiniotis's La Théorie de l'homotopie de Grothendieck (Grothendieck's Homotopy Theory): http://www.math.jussieu.fr/~maltsin/ps/prstnew.pdf
• Cisinski's (augmented version of his) thesis Les Préfaisceaux comme modèles des types d'homotopie (Presheaves as Models for Homotopy Types): http://www.math.univ-toulouse.fr/~dcisinsk/ast.pdf

See also

• Homotopy hypothesis

References

• http://mathoverflow.net/questions/58497/is-there-a-high-concept-explanation-for-why-simplicial-leads-to-homotopy-theo/
• http://mathoverflow.net/questions/171920/whats-special-about-the-simplex-category/172914
• R. Brown, The Origins of `Pursuing Stacks' by Alexander Grothendieck

External links

• http://ncatlab.org/nlab/show/Pursuing+Stacks
• http://mathoverflow.net/questions/115549/conjectures-in-grothendiecks-pursuing-stacks