nLab (2,1)-presheaf

Idea

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 $(2,1)$-presheaf such that the functors into its descent objects are full and faithful functors.

The ∞-stackification of a $(2,1)$-presheaf is a certain 2-sheaf or stack.

Related concepts

• (0,1)-presheaf

• presheaf

• (2,1)-presheaf

  presheaf of groupoids

  (2,1)-sheaf, 2-sheaf, indexed category, stack

• (∞,1)-presheaf

• (∞,n)-presheaf