The prosecutor's 'objection' was sustained. [=the judge agreed that the prosecutor was right to object]
She doesn't have any 'objection to' going. = She's made no 'objection to' going.
People have raised/voiced a number of 'objections to' the proposed changes.
(..) You'll have to excuse Dr. Cooper. He's been under a lot of, um... He's nuts. They'll come, they'll settle And I'll win the prize I don't understand your objections, Professor Goldfarb. Why wouldn't the Sonora Desert make a perfectly good Promised Land? Go away. We could call it Nuevo Jerusalem. (..)2008 TvShow: The Big Bang Theory Title: The Jerusalem Duality Season: 1 Episode 12