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".

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

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.