diagonal of a bisimplicial set

**(diagonal)**

For ${X}_{\u2022,\u2022}$ a bisimplicial set, its **diagonal** is the simplicial set that is the precomposition with $(\mathrm{Id},\mathrm{Id}):{\Delta}^{\mathrm{op}}\to {\Delta}^{\mathrm{op}}\times {\Delta}^{\mathrm{op}}$, i.e. the simplicial set with components.

$$d(X{)}_{n}={X}_{n,n}\phantom{\rule{thinmathspace}{0ex}}.$$

See also diagonal.

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