nLab
diagonal of a bisimplicial set

Definition

(diagonal)

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

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

See also diagonal.

Revised on April 18, 2013 18:50:16 by Tim Porter (95.147.236.226)