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"established a context" is correct and usable in written English.
You can use it when you want to describe a situation that provides a basis for further discussion or to describe a background to an activity or event. For example, "The presentation established a context for the group to discuss the new project."
Exact(2)
In every instance bass and drums established a context for Mr. Rivers's peregrinations.
Not only did it define an area of cultural enquiry that had hitherto barely existed; it also established a context that no discussion of the new wave of late-1950s northern writers - John Braine, Alan Sillitoe, Stan Barstow, Sid Chaplin - could ignore.
Similar(58)
It begins by establishing a context for the artist.
With these scenes, Freedman establishes a context for the often repeated thesis of his book.
This is partly to establish a context for the river or swamp or beach I'm visiting.
This instantly establishes a context of capitalist toil: ideal for a play about the difficulty of doing good in a wicked world.
Another posting explained that the assignment met writing standard E2c, which requires that students "produce a narrative account that energizes the reader by establishing a context, a conflict and provides a sense of closure to the writing".
In another, to establish a context of sadness, men watched a scene from the movie "The Champ" after sniffing tears or saline.
However, the BBFC states that the game – which involves chasing armed mercenaries through London Underground Tube carriages – establishes a context which may be "unsettling" and "upsetting".
The passage about being cool establishes a context for what the Rat tells J in Pinball, just before his final departure from J's Bar: "See, J, it doesn't work," he said.
In any case, I don't mean to be harsh, only to establish a context for my somewhat ambivalent admiration of "Something in the Air," the new film by Olivier Assayas (born in 1955), set in France in the early 1970s.
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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