This is _incredibly_ naive because I'm a total layman when it comes to both, but is there a relationship between category theory and semiotics? It seems like indexes and symbols are similar to categories and morphisms. Again, I really don't know what I'm talking about as I've barely scratched the surface of either but it would be awesome to hear from someone who does so they can tell me that I'm misunderstanding both things (and if I'm lucky, _how_ I'm misunderstanding them).
I don't have a clue about semiotics, but "The Adjunction Between Syntax and Semantics" [0] gets bandied about a lot in this space. There's also an attempt to use adjunctions to explain "generalization" which might be relevant [1]. Generally, "adjunctions are everywhere".
The relationship you're sensing appears very general, in the sense that "is there a relationship between Category Theory and Linguistics?" I definitely think there's a relationship because that's how the human intellect operates, everything is a relationship, but I do not think there is an intrinsic and meaningful relationship outside the context of general cognition.
I think Semiotics is important and the study of what the symbols in Category Theory are or why they are used is a meaningful study (and would enable a deeper understanding) but I don't think it's a prerequisite for comprehending Category Theory itself.
I figured that semiotics wouldn't at all be required to understand category theory (or vice versa). More that the general language of sign/signified and so forth feels similar in some vague way. But again, you're probably right in that the brain likes to find patterns even when they aren't really there.
