nLab diagonal of a bisimplicial set

Definition

(diagonal)

For $X_{\bullet,\bullet}$ a bisimplicial set, its diagonal is the simplicial set that is the precomposition with $(Id, Id) : \Delta^{op} \to \Delta^{op} \times \Delta^{op}$, i.e. the simplicial set with components.

$d(X)_n = X_{n,n} \,.$