The phrase "obsession on" is not grammatically correct in written English.
The correct phrase would be "obsession with." Example: Her obsession with her ex-boyfriend was becoming unhealthy.
In its nominal use, it frequently refers to a "fixation" or "obsession" on one aspect of something to the detriment of others.
This is the "they started it" school of right-wing thought: Right-wing commentators realize they're obsessed, but they blame their obsession on their lefty opponents.
"It's simply inappropriate to engage in self obsession on a spot that memorializes those who obsessed about others, and about mission, more than themselves," he wrote to me in an e-mail on Sunday.
Because once under its spell, the pursuit of Fame can become an obsession on the order of chasing the dragon, making one all too willing to sacrifice anything in order to obtain its fleeting and instantly addictive high.
Bundy is arguably the first serial killer to create the true crime obsession on a larger scale thanks to his trial being the first one televised in American history.
So he took his obsession on the road.
The obsession on just the exit, the money, makes me sad.
You see it in Industrie, with its obsession on behind-the-scenes mountain-movers.
Even in 1985, Kramer knew the effect of this obsession on others.
It's the news sensation of the world, the subject of obsession on television and online.
