I am only a novice with Category Theory but that statement has me wondering why you say that. Do you have references to papers noting the same? While most of what a programmer reads about Category Theory will relate Category Theory to functions, do not take that to mean that Category Theory can only do functions.
In researching the touch points between Category Theory and programming many years ago for my own benefit, I found that a lot of it flows though one common touch point found by Eugenio Moggi. I won’t give you any more details so that you can see if you can find the touch points and then hopefully learn why, when programmers talk about Category Theory, that the work of Eugenio Moggi seems to be a strange attractor. When you come at Category Theory from the view of someone with a PhD. in Computer Science who studies it, you will get a different view and if you come at Category Theory from the view of of someone with a PhD in Math you will get still another view.
You really should read some of those references I left. I took sometime yesterday to peruse the Q&A and some answers have very good details related to the touch points between Category Theory and what you seek. However there were some other specific questions I was surprised that were not asked.