[[!redirects (∞,n)-topos]] +-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Higher category theory +--{: .hide} [[!include higher category theory - contents]] =-- #### Higher topos Theory +--{: .hide} [[!include (infinity,1)-topos - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Definition For $\mathbf{H}$ an [[(∞,1)-topos]] and $n \in \mathbb{N}$, the collection $n Cat(\mathbf{H})$ of [[n-category object in an (∞,1)-category|n-category object in]] $\mathbf{H}$, hence of [[(∞,n)-sheaves|(∞,n+1)-sheaves]] on $\mathbf{H}$ is an $(\infty,1)$-localic $(\infty,n+1)$-topos. See at _[Internal category object in an (∞,1)-category -- Iterated internalization](category+object+in+an+%28infinity%2C1%29-category#InternalnCategories)_. ## Related concepts * [[directed homotopy type theory]] * [[locally presentable (∞,n)-category]] [[!include flavors of higher toposes -- list]] [[!redirects (∞,n)-toposes]]