A simplicial complex is a PL structure for, and thus also homeomorphic to, a manifold if the link of every vertex is a simplicial sphere, for which there exists a definition. (I know that for high dimension, the definition might be untractable to check.) My question now is the same for simplicial sets.
Take for example the simplicial set with one vertex and one nondegenerate edge starting and ending at the vertex. Obviously, the geometrical realisation is $S^1$, but the link of the vertex is empty. In this case, the definition for a simplicial manifold fails.
I would be especially interested in a categorical definition, that is, one in terms of the simplicial set as a functor without much reference to its components.
Edit: I've clarified the question after a few years.