One is to take the morphisms $\mathbb{Z}/n\mathbb{Z} \to \mathbb{Z}/m\mathbb{Z}, m | n$ given by sending $1$ to $1$. This gives a diagram (inverse system) whose limit (inverse limit) is the profinite completion $\hat{\mathbb{Z}}$ of $\mathbb{Z}$. This diagram also makes sense in the category of unital rings, since they also respect the