Sharing the same photos AND the same catalog (the database) is done by storing both on an external drive that you plug alternatively to each computer. The typical use is to have your library available instantly in a desktop or in a laptop when you go away. You only have to create a full backup on a dedicated backup external drive, followed by a restore to the destination external drive. Anything you do on a computer is immediately available to the other one.
However, sharing the same catalog between two persons is different than using two computers alternatively from the same person. Anything the first user does (including tagging, deleting, renaming or moving in the folder tree) is also done for the other user.
So, there are other ways including doing the backup and restoring directly into the secondary computer. The problem is that you can't easily 'update' the second computer: you have to repeat the backup and restore each time, which takes time (and disk space to create an updated photo folder tree and a new catalog before removing the old one for more safety).
A possible compromise would be to move the photos and the catalog to an external drive and also use the direct backup to the laptop at regular intervals.
- The library copy on the laptop is independent and does not imply risks for the 'master' library on the external drive. You can create different catalogs locally from copies of the original. You don't need access to the master external drive most of the time for mailing or browsing, except for the most recent photos. A plus for this solution is that the copy is a very useful backup in addition to the dedicated backup external drive.
- If you need instant update of the master library, just plug in the master external drive.