I think Jared answered Charlie's question just fine. I find terminology like "systems" and "connections" a bit annoying here because later in the book one sees a more precise treatment of these ideas using more standard, and more precisely defined, terminology.
As Jared already knows, when we get serious we use the term "partition" instead of "system". Charlie: we'll explore partitions in detail here:
* [Lecture 10 - Chapter 1: The Logic of Partitions](https://forum.azimuthproject.org/discussion/1963/lecture-10-the-logic-of-partitions/p1)
* [Lecture 11 - Chapter 1: The Poset of Partitions](https://forum.azimuthproject.org/discussion/1991/lecture-11-chapter-1-the-poset-of-partitions/p1)
* [Lecture 12 - Chapter 1: Generative Effects](https://forum.azimuthproject.org/discussion/1999/lecture-12-chapter-1-generative-effects/p1)
* [Lecture 13 - Chapter 1: Pulling Back Partitions](https://forum.azimuthproject.org/discussion/2008/lecture-13-chapter-1-pulling-back-partitions/p1)
However, it would be unwise to read these lectures until you've read the previous ones!