Shared libraries are shared in RAM between processes. But I believe the cache for each process is not shared. If three processes currently have the same shared

Shared libraries are shared in RAM between processes. But I believe the cache for each process is not shared. If three processes currently have the same shared lib code (or any shared memory) in their working set, they will each work it into cache independently. This sounds inefficient but is rare in practice and maintains process isolation. The added complexity of cache sharing would not be worth it. If I have this wrong, someone please correct me.