nLab cubical object in an (infinity,1)-category

Idea

Let $\Box$ denote a category of cubes, and let $C$ be an $(\infty,1)$ -category.

A cubical object in $C$ is an (∞,1)-functor

X \colon \Box^{op} \to C

from the opposite category of $\Box$ into $C$ .

The $(\infty,1)$ -category of cubical objects in $C$ and morphisms between them is the (∞,1)-category of (∞,1)-functors

C^{\Box^{op}} = Func_\infty(\Box^{op}, C) \,.

If $C$ is 1-truncated, then a cubical object in $C$ is just a cubical object in the traditional sense of category theory.

Created on April 9, 2025 at 16:51:41. See the history of this page for a list of all contributions to it.