Could you elaborate a bit on this. Sounds like an interesting take.

When I'm mapping out a narrative arc, sometimes I will want to indicate that some action is monotone or idempotent, or that it is isomorphic or reversible from some other state. Those properties end up being path equivalences.

Similarly, sometimes there can be multiple social relations between characters within a narrative setting; somebody might be both a friend and a parent, for example. Properly modelling this requires allowing multiple distinct edges between vertices.

And, finally, technically any hypergraph with path equivalence is a category.

When I'm doing narrative analysis on a whiteboard, the diagrams that I draw are category-theoretic, not graph-theoretic, and I'd like to be able to bring that richness into my narrative-mapping tool without having to flatten everything down into annotated graphs.

I need to think a bit more about what you are saying. This is a very interesting point of view. Can I come back to you on this?

Don't worry about me specifically. https://arxiv.org/abs/1706.00526 is more food for thought, if you need it.

Thanks. Any feedback, pointers to additional resources and so forth... it's all greatly appreciated.

With regards to multiple distinct edges between vertices: TopicDB (https://github.com/brettkromkamp/topic-db) already allows this. However, in my drive to simplify from a user-perspective, there is no corresponding GUI. A possibility would obviously be to provide both the current simplified GUI (by default) and an advanced GUI (allowing for multiple edges between vertices). I'm actively considering this as multiple people have mentioned/requested it.