LR does not sync computer-to-computer. It is designed as a single-computer, single-user system.
The easiest way to "share" the catalog between multiple of your computers is to put the catalog and presets (and optionally the images) on an external drive and move the drive from computer to computer as needed; thus no actual sharing.
You can also copy the catalog from computer to computer across a network.
Alternatively you can select the images you want to share, "export as catalog", copy the small catalog to the other computer, "import from catalog".
thanks for your reply. I'm aware of the no-sync feature between two computers and the possibility to have the catalog on an external drive. I thought there might be the option now with creative cloud to work at home on a collection and then take my macbook with me on a business trip to then continue the work. The same way I can work on the ipad and then carry on at home on the desktop. It's in the cloud, so why not be able to continue editing in any other Lightroom facility?
It probably has to do with the syncing of limited image quality files and the limited editing abilities in the mobile version of LR. Lightroom is still a single-computer system.