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The Library screen in the Apple TV app includes your purchases and rentals, organised by category.
If you’ve set up Family Sharing with your Apple ID account, your other family members’ purchases appear in Library. You can easily switch to another person’s collection.
See Family Sharing on Apple TV.
In the Library screen of the Apple TV app , select Family Sharing, then select a family member.
When you find what you want to watch, select it, then select Play.