In mathematics, especially algebraic geometry and algebraic topology, a higher stack is a higher category generalization of a stack (a category-valued sheaf). The notion goes back to Grothendieck’s Pursuing Stacks.1
Toën suggests the following principle:2
As 1-stacks appear as soon as objects must be classified up to isomorphism, higher stacks appear as soon as objects must be classified up to a notion of equivalence which is weaker than the notion of isomorphism.
Sometimes a derived stack (or a spectral stack) is defined as a higher stack of some sort.
References
References
- Töen 2014, § 1. Selected pieces of history.
- Bertrand Toën, Higher and Derived Stacks: A Global Overview, arXiv:math /0604504
- Carlos Simpson, Algebraic (geometric) n-stacks, 1996, arXiv:alg-geom/9609014.
- André Hirschowitz, Carlos Simpson, Descente pour les n-champs (Descent for n-stacks), 1998, arXiv:math/9807049.
- Töen, Bertrand (2014). "Derived algebraic geometry". EMS Surveys in Mathematical Sciences. 1 (2): 153–240. arXiv:1401.1044. doi:10.4171/EMSS/4.
Further reading
Further reading
- https://ncatlab.org/nlab/show/higher+stack
- David Carchedia, On the étale homotopy type of higher stacks, Higher Structures 5(1):121–185, 2021. [1]
- https://math.stackexchange.com/questions/2493119/higher-stacks-and-bg