Transfors between 2-categories
Morphisms in 2-categories
Structures in 2-categories
Limits in 2-categories
Structures on 2-categories
(∞,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
A (2,1)-presheaf is a presheaf with values in the (2,1)-category Grpd. A 2-truncated (∞,1)-presheaf.
Sometimes this is also called a prestack. Other times a prestack is more specifically taken to be a separated (2,1)-presheaf: a -presheaf such that the functors into its descent objects are full and faithful functors.
The ∞-stackification of a -presheaf is a certain 2-sheaf or stack.