nLab rectified infinity-stack

An ∞-stack on a (∞,1)-category-domain $C$ that happens to be an ordinary category (i.e. not a derived stack) is rectified if it is an ordinary functor $C^{op} \to$ SSet instead of a general (∞,1)-functor (i.e. pseudofunctor).

A central theorem about the model structure on simplicial presheaves says that rectified ∞-stacks are sufficient: they already present the full (∞,1)-category of (∞,1)-sheaves (= ∞-stacks).

Notice that, by a result recalled at descent for simplicial presheaves, a rectified $\infty$-stack $A$ is an ∞-groupoid internal to (pre)sheaves satisfying a descent condition.

Examples

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