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Is it ok to set up the db in a cloud, like what you do in the local?
Probably not.
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... with the my.ini file setting the basedir and datadir in the cloud, and access from other computer with the cloud linked in?
... if the cloud is synced to the computer
Absolutely not.
Database != File
Please,
please,
stop thinking of your Database as a File.
Your Database is a
running process, most of which exists only
in memory, not on disk at all.
No file synchronising program is going to be able to
reliably transfer changes from one set of database files to another.
Every DBMS has its own way of replicating [logical] changes between databases, and trying to unpick changes flying around at the data file level is
not one of them.
If you
have a hosting company, then get them to host the entire Database and simply
connect to that Database from applications running on your [many] computers.
Regards, Phill W.