In a case like this it's interesting which case is used as a definition and which cases are considered to follow from that. I personally found the idea of the 2-section's cliques to be contained by an edge in H to be the most intuitive. When I was thinking through what the original definition meant, I ended up translating it into that before I moved on to the next section and saw it was going to be a theorem.
![Hypergraph Cartesian Product [Hypergraph Theory, Ep. 11]](http://i.ytimg.com/vi/u1vp88bglAc/mqdefault.jpg)
![Hypergraph Cartesian Product [Hypergraph Theory, Ep. 11]](/img/tr.png)
![Introduction to Hypergraphs [Graph Theory]](http://i.ytimg.com/vi/UwvZn9lm_98/mqdefault.jpg)
In a case like this it's interesting which case is used as a definition and which cases are considered to follow from that. I personally found the idea of the 2-section's cliques to be contained by an edge in H to be the most intuitive. When I was thinking through what the original definition meant, I ended up translating it into that before I moved on to the next section and saw it was going to be a theorem.