Generalization of hypergraphs with edges to edges (and relationship to higher categories)?

Question

For some authors, it seems that hypergraphs allow or do not allow edges on edges, but it's hard to find a lot of literature on the topic. I am wondering if hypergraphs with edges on edges had a specific name, or what to look for in literature.

Also, I can see this kind of recursive structures in other areas of maths, the first two that comes to mind being:

• Higher categories with (n+1) morphisms on (n) morphisms
• Polytopes with (n+1)-dimensional faces built upon (n)-dimensional faces (3D cell -> 2D faces -> 1D edge -> 0D vertex)

My questions are:

1. Is there any literature on hypergraphs with edges on edges?
2. Do they have a specific name?
3. Is there any general abstraction for recursive structures in maths like hypergraphs with edges on edges/higher categories/polytopes?