# Series-parallel DAG characterization

According to this Wikipage series-parallel graphs are characterized like this:

2-connected series-parallel graphs are characterized by having no subgraph homeomorphic to $$K_4$$.

I couldn't find a similar characterization for series-parallel directed acyclic graphs (DAGs), however I think that the prohibited subgraph in this case can be a little simpler ($$K_4$$ minus one edge plus specific orientation):

Is it correct? Is it proven anywhere?