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Tom Leinster, How I Learned to Love the Nerve Construction, blog
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
The associated paper is
These ideas are clarified and expanded on in
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