nLab n-topos

Idea

An $n$-topos is an n-category analog of a topos.

An $n$-topos that is an (n,1)-category, hence where all k-morphisms for $k \geq 2$ are equivalences is called an (n,1)-topos. See there for more.

Examples

For every $n$, The canonical $(n+1)$-topos is nCat?, the (n+1)-category of n-categories.

Related concepts

flavors of higher toposes

• 1-topos

  • (0,1)-topos

  • (1,1)-topos = topos

  • (2,1)-topos

  • $(n,1)$-topos

  • (∞,1)-topos ($n$-localic)

    $\;\;\;\;$ model topos

• 2-topos

  • (2,2)-topos ($n$-localic)

  • (∞,2)-topos

• $n$-topos

  • $(\infty,n)$-topos

References

• Michael Shulman, n-topos for large n .