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Actually, if two closed instances with instance-public libraries want to talk, every user has to follow every library they know on the other instance. It could be enhanced if instances (as ActivityPub actors, probably) could emit follow requests, that could be understood as "Hi, would you like to share this library with all my local users?". Also, a user could emit a follow request to an entire instance. If accepted, every library shared with the entire instance could (we could add a new option "everyone on this instance can see this library, also people following this instance could access it too") be read by this user. Finally, an instance could follow an instance, making all libraries published with the corresponding privacy setting be available to all users on the first instance.

Also, Users could be followed on this same system, and not only libraries. Thus, all libraries having the required privacy setting from an user could be followed at once

So, in short:

• Users could follow Instances (and access all the instance-wide libraries in the followed Instance)
• Users could follow Users (and access all their instance-wide libraries)
• Instances could follow Libraries (and make those available to all their local Users)
• Instances could follow Users (and make all their instance-wide libraries available to all their local Users)
• Instances could follow Instances (and make all the instance-wide libraries on the instance available to all their local Users)
• Users could choose a new privacy setting for Libraries: "Share on everyone on this instance, and accept to be shared by the Instance"
• There would be a new type of follow, asking to share multiple Libraries.