nLab (n,1)-sheaf

Definition

For $n \in \mathbb{Z}$, $-2 \leq n \lt \infty$, an $(n,1)$-sheaf is an n-truncated (∞,1)-sheaf: an (∞,1)-sheaf with values in n-groupoids.

This is also sometimes called an $(n-1)$-stack.

Examples

• (0,1)-sheaf = ideal (of a poset/proset)

• (1,1)-sheaf = sheaf

• (2,1)-sheaf = stack (of groupoids)

Related concepts

• n-truncated object in an (∞,1)-category

• model structure for homotopy n-types