Photos app single library with Sierra and High Sierra I have two Macbooks, one is running High Sierra, and one is running Sierra. My problem is, that I cannot open my Photos library with Sierra since I've opened it with High Sierra, it says that I need to update my Photos app.

Is there a way to update this app without changing the OS?
No - you'll need to restore the photo library and associated files back to a time before the migration / upgrade happened. The database schema and many other items like face recognition databases are one way forward upgrades.

If you don't have a backup, you would need to install High Sierra on an external drive - open the Photos library and then try syncing it back to iCloud (unlikely to work, but maybe try on a small library first) or export all of the photos to the filesystem and then walk away from the library.

When you go back to Sierra you'd need to make a new library and then import the photos from the filesystem. This would be a lot of work and you might have more problems with things like memories / albums / edits than the reversion to Sierra cures.