nLab cubical object

Idea

A cubical object in a category $C$ is a functor

$$F : \Box^{op} \to C$$

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

If $C = Set$ then this is called a cubical set.

Functors

$$F : \Box \to C$$

from the cube category itself are co-cubical objects in $C$.

Related concepts

• simplicial object.

• ´cubical set

• model structure on cubical presheaves

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