nLab
bisimplicial object

Definition

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

$$F:{\Delta }^{\mathrm{op}}\times {\Delta }^{\mathrm{op}}\to C$$F : \Delta^{op} \times \Delta^{op} \to C

where $\Delta$ is the simplex category.

This is the same as a simplicial object in the category of simplicial objects in $C$.

Examples

• bisimplicial set

• bisimplicial group

Related concepts

• simplicial object