[The_Colonel]

It's not the idea itself which seems to me absurd, it's the process - let's take something from abstract mathematical field and apply it on a vaguely "topologically" similar subjective experience and think that "it's proven by math".

[exolymph]

Topological similarities can be meaningful. Shape and structure are like form and function.

[The_Colonel]

Topological similarities can be meaningful as in they often provide great source of inspiration.

However, it's just an inspiration and it must be proven in its newly applied field - proof in context of category theory is not valid in the context of inter-personal relations.