The phrase "admonition about" is correct and usable in written English.
It can be used when referring to a warning or caution regarding a specific topic or issue.
Example: "The teacher gave an admonition about the importance of studying for the upcoming exam."
Alternatives: "warning regarding" or "caution about".
He's trying to hammer home his admonition about change, while assiduously creating an image of being tough, capable and unrelenting.
And as Mr. O'Brien's admonition about political advantage suggests, there is nothing guaranteed, or permanent, about the outcome.
The three-judge panel acknowledged the Supreme Court's admonition about the limited precedential value of Bush v. Gore.
We might dread every deceased follicle in light of Matthew's admonition about our looming mortality: "And even the very hairs on your head are numbered".
But Tagliabue's admonition about how best to change a culture was also pointed: next time try a velvet glove, he was advising Goodell, instead of a hammer.
Eyes wide open, with his eyebrows slightly raised, the scribe presses his lips as if he had just been given an admonition about his performance.
But his admonitions about Indocin and Mobic were largely ignored.
Their admonitions about America's burgeoning consumer society are strikingly different from Mr. Brooks's amused welcome.
The state parties and presidential candidates routinely ignore the RNC's admonitions about the primary calendar, for example.
The ever-optimistic Mr Gore claimed that Li Peng, China's stony-faced prime minister, had been "receptive" to admonitions about human rights.
"How many of you have discussed Mr. Orsini's letter with your parents?" asked Annie Thurston, one of the eighth graders, referring to his admonitions about online activity.
