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.
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.