>In more formal set theory we might identify you by numbers.
So in this case, we can have the objects be a set of numbers or equivalently identification using numbers can also be written as an arrow for example called employee ID. So what I was curious about was(with hopefully better wording than before) when dealing with categories or functors, must we write anything that can be written as arrows as arrows or can we just keep it inside the object?
But I think I get your point. I guess when writing any of this out you must use something to represent the object which includes using a dot like I was thinking but that is arbitrary of the writer... which made me realize the database schema is actually the "amorphous blob" that I had in mind on more levels than I had initially thought since categories are also objects. Now I can see why they call them categories.