nLab higher stack

Idea

Classically, the theory of stacks was motivated by the study of moduli problems for which objects are classified up to isomorphism. Higher stacks are a generalization where objects are classified up to some notion of equivalence, like complexes up to quasi-isomorphism, topological spaces up to weak homotopy equivalence, or abelian categories up to equivalence of categories.

See also

• stack
• n-stack
• infinity-stack
• derived stack
• derived algebraic geometry

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.