double nerve



The double nerve of a 2-category CC is a bisimplicial set obtained by regarding CC 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.


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

Last revised on November 17, 2009 at 20:53:14. See the history of this page for a list of all contributions to it.