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.

…

Last revised on September 4, 2013 at 13:58:46. See the history of this page for a list of all contributions to it.