Pursuing Stacks
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Pursuing Stacks (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.
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
- Derivator, a concept introduced in the manuscript
- Test category, this was also introduced there
References
- http://mathoverflow.net/questions/58497/is-there-a-high-concept-explanation-for-why-simplicial-leads-to-homotopy-theo/
- R. Brown, The Origins of `Pursuing Stacks' by Alexander Grothendieck
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