structures in a cohesive (∞,1)-topos
(Here denotes the sieve associated to the cover).
The term prestack is used in two different ways in the literature: some authors use it synonymously with just (2,1)-presheaf, others with separated -presheaf .
Let Mfd be the site of topological manifolds. Let be a topological group and the (2,1)-presheaf on represented by the nerve of the delooping-groupoid (see simplicial group for te notation). Let be the (2,1)-sheaf of all -principal bundles. This is the (2,1)-sheafification of . The canonical morphism
includes over each the single object of as the trivial -principal bundle. Its automorphisms are given by continuous functions . This is the same on both sides, hence is a full and faithful functor and is a separated -presheaf.