The .dropbox.cache folder is probably hidden. Turn on Show hidden items in the File Explorer, and it should display.
While it is possible to have the catalog in a Dropbox folder (requires a lot of caution and following some rules strictly), the cache folder is not the place to keep it. This folder is used internally by Dropbox, and should not be used for anything else.
I have a folder on Dropbox named Lightroom where I keep the catalog folder.
To avoid catalog corruption and other problems, the following rules must be followed strictly.
Before turning the computer off, make sure LrC is closed, and wait for Dropox to finish syncing. Do NOT turn the computer off before Dropbox has finished syncing.
After turning the computer on, Dropbox has to finish syncing before you launch LrC. Do NOT launch LrC before Dropbox has finished syncing.
In Dropbox preferences > Sync, Save hard drive space automatically must be turned off. Default sync state for new files must be set to Available offline.
The path to Dropbox must be the same on all computers that you use. If it is D:\Dropbox on your main computer, it must be the same on your other computers.
When I reconnected the 4 to drive after getting back home it would no longer link to the catalog. By @philr51159246
When you connect an external drive, Windows will assign the first available letter in the alphabet, which may not be the same letter the drive had the last time it was connected.
For instance, it the drive letter was previously D, and Windows assigned E, LrC will not be able find neither the catalog nor the images. (if they are on the same drive)
It is possible to change the drive letter back to what it was, if the letter is available, or assign a letter at the end of the alphabet, which is not likely to get changed. However, this could create issues for Dropbox if its path points to a different drive.
Please give us some details about your workflow.
Do you have one or several computers that you use with Dropbox?
Is the catalog as well as the images on Dropbox?
And are the catalog and images on an external drive that you move between computers?
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