higher stack
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.{{harvnb|Töen|2014|loc=§ 1. Selected pieces of history.}}
Toën suggests the following principle:Bertrand Toën, Higher and Derived Stacks: A Global Overview, arXiv:math /0604504
{{blockquote|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
{{reflist}}
- 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.
- {{cite journal | first = Bertrand | last = Töen | author-link = Bertrand Toën | title = Derived algebraic geometry | journal = EMS Surveys in Mathematical Sciences | volume = 1 | issue = 2 | year = 2014 | pp = 153–240 | doi = 10.4171/EMSS/4 | url = https://ems.press/journals/emss/articles/12837 | arxiv = 1401.1044 }}
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. [https://higher-structures.math.cas.cz/api/files/issues/Vol5Iss1/Carchedi]
- https://math.stackexchange.com/questions/2493119/higher-stacks-and-bg
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