Higher stack

Toën suggests the following principle:

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 is defined as a higher stack of some sort.

References

• 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.
• Bertrand Toën, Higher and Derived Stacks: A Global Overview, arXiv:math /0604504

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]