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Naso (Nov 09 2021 at 14:17):Is it right that a subobject of the nerve of a category is not necessarily a nerve? or even a quasicategory?
Reid Barton (Nov 09 2021 at 14:41):Sure, the nerve of a category is determined by its 2-skeleton, but will typically have nondegenerate simplices in all dimensions. If we remove all nondegenerate simplices starting in some dimension , then it won't be a nerve any more (since we didn't change the 2-skeleton) or even a quasicategory (because we removed an -simplex that was the unique solution to a horn-filling problem whose input involved only simplices below dimension ).