nLab (infinity,n)-sheaf

Definition

For $\mathbf{H}$ an (∞,1)-topos and $n \in \mathbb{N}$, an $(\infty,n+1)$-sheaf on (an (∞,1)-site of definition of) $\mathbf{H}$ is an n-fold category object in $\mathbf{H}$, $X \in n Cat(\mathbf{H})$.

See at Internal category object in an (∞,1)-category – Iterated internalization.

The collection of all $(\infty,n)$-sheaves is an (∞,n)-topos.

Related concepts

• sheaf

• 2-sheaf, (2,1)-sheaf

• (∞,1)-sheaf / ∞-stack

• (∞,2)-sheaf

• directed homotopy type theory