nLab
rectified infinity-stack

An ∞-stack on a (∞,1)-category-domain CC that happens to be an ordinary category (i.e. not a derived stack) is rectified if it is an ordinary functor C op 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 AA is an ∞-groupoid internal to (pre)sheaves satisfying a descent condition.

Examples

Revised on September 4, 2013 13:58:46 by Urs Schreiber (212.238.84.235)