You have thought about the language analogy much harder than I did. I will think about how to avoid this issue better in the future, so thank you. In any case, don’t stress it too much—all that this post seeks to establish is that category theory is a mathematics of “stuff taking action on stuff”—moreover, it does so in a logical, intuitive way that you are already familiar with, even if you don’t know higher maths. Judging by Said’s comment, I also should have clarified that specific branches of mathematics fill in particular things for “stuff” and “taking action.” E.g., you get set theory when you fill in “sets” for stuff and “functions” for taking action.
It might get weird for me as part of the past prgoress for me is how functions are actually objects ie non-verblike. You can example code a function into ordered pairs which can be represented as a set. You are meaning more in the sense that a function by itself is missing something has a “hole” in it? For example “It rains” can seem like a language construction where “rain” appears without holes (and in my native language you express that kind of thought without any formal subject, “rains” is a pertfectly fine sentence that descripbes a common wheather condition/activity.).
You have thought about the language analogy much harder than I did. I will think about how to avoid this issue better in the future, so thank you. In any case, don’t stress it too much—all that this post seeks to establish is that category theory is a mathematics of “stuff taking action on stuff”—moreover, it does so in a logical, intuitive way that you are already familiar with, even if you don’t know higher maths. Judging by Said’s comment, I also should have clarified that specific branches of mathematics fill in particular things for “stuff” and “taking action.” E.g., you get set theory when you fill in “sets” for stuff and “functions” for taking action.
It might get weird for me as part of the past prgoress for me is how functions are actually objects ie non-verblike. You can example code a function into ordered pairs which can be represented as a set. You are meaning more in the sense that a function by itself is missing something has a “hole” in it? For example “It rains” can seem like a language construction where “rain” appears without holes (and in my native language you express that kind of thought without any formal subject, “rains” is a pertfectly fine sentence that descripbes a common wheather condition/activity.).