Photos was unable to repair permissions on your library

If each of you are accessing both libraries in the Shared folder that's why you're having problems. Some time ago, before Mavericks, using the Shared folder with iPhoto (and now Photos) for sharing a library was discontinued. Each time one accesses the library the permissions on the new or modified files are changed and locks out the other user.

The only solution is to put both of the libraries on an external HD that is formatted OS X Extended (journaled) with Ownership set to be ignored and connected via Firewire, USB or Thunderbolt:

This will let both of you use each of the libraries without access problems.

this article explains (yes it is for iPhoto but holds true for Photos too) - iPhoto: Sharing libraries among multiple users - Apple Support

LN

I had a similar message. I don't know what caused it, but I found another solution that does not require a new drive. First I ran iPhoto (yes it is still there in the application folder), It established a newly modified version of my old iPhoto library that was not the same as the inaccessible System Photo Library. Then I clicked Photos while holding the option key. That gave me a choice of libraries and I chose the new version of the iPhoto library instead of the System Photo Library. I also deleted the old System Photo Library that had become inaccessible. I then ran Photos and it opened with no error message and proceeded to convert the iPhoto library into a Photos library. When the app opened with the new library, It did not include any shared photos, but that was solved by going to Photos general preferences and designating the new current library as the System Photo Library. I then turned on sharing (which only works in the System Photo Library) and everything populated itself.

Had the same problem. Error message was : Photos was unable to repair permissions on your library.

I held down Option while opening Photos and it gave me a list of the photo libraries. Clicked on the correct one and it worked perfectly.

Easy fix (for once)