How to Think About Finite Factored Sets?

In general, want to work with a pair s coma b, where s is a set, a finite set, and b is a factorization of s. For any point in s, you can kind of uniquely specify it by specifying its kind of value on each of the basis partitions. So ys into a question i have, which is, how should i think about the factors here, like these finite factored sets? I guess they 're supposed to represent, like, what's going on in the world? And so s kind of a choice of what comes first,What are the primitive variables in your structure?