## References ### General theory of realization-and-nerve * [[nLab:Tom Leinster]], _How I learned to love the nerve construction_ (2008) ([blog](http://golem.ph.utexas.edu/category/2008/01/mark_weber_on_nerves_of_catego.html)) The associated paper is * [[nLab:Mark Weber]], _Familial 2-functors and parametric right adjoints_ (2007) ([tac](http://www.tac.mta.ca/tac/volumes/18/22/18-22abs.html)) These ideas are clarified and expanded on in * [[nLab:Clemens Berger]], [[nLab:Paul-André Melliès]], [[nLab:Mark Weber]], _Monads with Arities and their Associated Theories_ (2011) ([arXiv:1101.3064](http://arxiv.org/abs/1101.3064)) * [[nLab:monad with arities]] ### Particular instances * Emily Riehl, Understanding the Homotopy Coherent Nerve, [blog](http://golem.ph.utexas.edu/category/2010/04/understanding_the_homotopy_coh.html) * nerve of a graph, at [[Segal condition]] * [[nLab:complicial set|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 [[nLab:Segal condition]] * For further relations between nerves and Segal condition, see [[nerves and Segal conditions]]