Suppose that we have a partially ordered set $(X,\leq)$ such that the following condition holds:
There exists a disjoint partition $X = \bigcup_{ i \in \mathbb N_0 } X_i$ such that for $i < j$ we have $ \forall x \in X_i, y \in X_j : x_i < x_j$.
The principal example is of course any simplicial complex, where the $X_i$ correspond to simplices of dimension $i$.
So a partially ordered set with "levels" is a very common structure. What is the canonical term (there should be one) for such a structure?