nLab double nerve

Idea

The double nerve of a 2-category $C$ is a bisimplicial set obtained by regarding $C$ as a Cat-enriched category or a Cat-internal category and then applying the ordinary nerve operation to each hom-object category to obtain first a simplicially enriched category and then to apply the obvious nerve operation again to obtain a bisimplicial set.

References

See for instance page 227 of

• M. Bullejos, E. Faro, V. Blanco, A full and faithful nerve for 2-categories (arXiv)

or page 39 of

• A. Cegarra and J. Remedios, The relationship between the diagonal and the bar constructions on a bisimplicial set Topology and its Applications Volume 153, Issue 1, 1 August 2005, Pages 21–51