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The phrase "monopoly over" is correct and usable in written English.
You can use it to describe a situation where one person or organization has exclusive control over an industry, product, or service. For example, "The government has a monopoly over the television broadcasting industry, so all TV channels must be licensed by them."
Exact(59)
The party ceded its monopoly over public messages.
Costliest of all is the state monopoly over oil.
It enjoys a monopoly over exports of the stuff.
France's 9,000 notaires enjoy a monopoly over property conveyancing.
Popular fury confronts the state's monopoly over force.
Amtrak was given a monopoly over intercity rail service.
"It hurts my leverage if the shoe company has a monopoly over advertising dollars".
Each state typically grants a single company a monopoly over telephones in any given prison.
Obviously, the locals would be delighted to be given a Mamirauá-like monopoly over the trade.
Some farmers complain of the state's continuing monopoly over inputs and sales.
This was a somewhat cryptic statement — doesn't every company have a monopoly over its own products?
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com