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homotopy theory, (∞,1)-category theory, homotopy type theory
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A version of the nerve of a category for 2-categories:
The double nerve [Bullejos, Faro & Blanco 2005 p 227, Cegarra & Remedios 2005 p 39] of a 2-category is the bisimplicial set obtained by regarding 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.
Manuel Bullejos, E. Faro, V. Blanco, page 227 (5 of 11) in: A full and faithful nerve for 2-categories, Appl Categor Struct 13 (2005) 223–233 [arXiv:math.CT/0406615, doi:10.1007/s10485-005-2957-6]
Antonio Cegarra, Josué Remedios, page 39 (19 of 31) of: The relationship between the diagonal and the bar constructions on a bisimplicial set, Topology and its Applications 153 1 (2005) 21-51 [doi:10.1016/j.topol.2004.12.003]
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