(∞,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
Write for the category ∞Grpd of -groupoids regarded as an (∞,1)-category.
Let be a simplicial set (which in particular may be a quasi-category).
An -presheaf on is an (∞,1)-functor
The (∞,1)-category of -presheaves is the corresponding (∞,1)-category of (∞,1)-functors
Section 5.1 of