Not a Mathematician and one should chime in. The relationship you're sensing appears very general, in the sense that "is there a relationship between Category

Not a Mathematician and one should chime in. 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.