General theory of realization-and-nerve

The associated paper is

  • Mark Weber, Familial 2-functors and parametric right adjoints (2007) (tac)

These ideas are clarified and expanded on in

Particular instances

  • Emily Riehl, Understanding the Homotopy Coherent Nerve, blog

  • nerve of a graph, at Segal condition

  • Complicial sets are precisely those simplicial sets which arise as the omega nerve of a strict omega-category.

  • A simplicial set is the nerve of a category precisely if it satisfies the Segal condition, at nerve

  • (Nerve Theorem, Segal 1968): A simplicial set is the nerve of a small category precisely if it satsfies the Segal conditions. See the reference at Segal condition

  • For further relations between nerves and Segal condition, see nerves and Segal conditions

Last revised on November 13, 2012 at 15:07:23. See the history of this page for a list of all contributions to it.