How to share a library between two computers
For this to work, both computers need to have access to a common hard drive so you can put the Pedia folder in a public folder. To simplify this how-to, we'll call the two computers one and two.

1) Make sure the Pedia program is not running. Then move the data folder, by default located in your Home folder under User/Library/Application Support/[Name of the Pedia], to the desired new location.

2) Then hold down the option key and start up the Pedia program on computer one. This will prompt you to choose a database. Choose the data folder you just moved to the new location.

3) Now do the same with computer two and choose the same folder that computer one is using.

data folder location

NOTE: If you ever forget where you have put the data folder, you can see the path in Preferences/General.