(∞,1)-category of (∞,1)-sheaves
Extra stuff, structure and property
locally n-connected (n,1)-topos
locally ∞-connected (∞,1)-topos, ∞-connected (∞,1)-topos
structures in a cohesive (∞,1)-topos
-Stackification is another term for (∞,1)-sheafification. It is the direct (∞,1)-categorical analog of the following 1-categorical situation.
Recall that for a site, sheafification is the functor
which sends every presheaf on to another presheaf which is weakly equivalent to with respect to the homotopical category structure on induced from the Grothendieck topology on . The presheaf respects weak equivalences and satisfies descent in that the hom-functor sends weak equivalences (the local isomorphisms) to weak equivalences.
Essentially by definition (according to Higher Topos Theory) the situation for -stacks is entirely analogous, as described at (∞,1)-category of (∞,1)-sheaves.
(Noticing that “-stack” is synonymous to “(∞,1)-sheaf”, “-stackification” to “-sheafification”, and so on.
For instance section 6.5.3 of
Revised on April 30, 2012 13:59:52
by Urs Schreiber