Is there a special name for a direct system where all the maps are injections?
It seems like people often write the direct limit of such a system as a union: e.g., "$S_\infty = \cup_{n=1}^{\infty} S_n$," where $S_n$ are the finite symmetric groups, and $S_\infty$ is the group of permutations of $\{1,2,\ldots\}$ which fix all but finitely many elements.
This union notation is intuitive, but I wonder if there is a more formal name/notation for this situation. Obviously, it is the simplest kind of direct limit to think about.