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.
(..) stirs her little heart. You have better luck with falcons. She'll never call you "Dainty face." Any objections? Of course not, my lord. He's just a slave. Let's go ashore and take her along. She stays here. (..)1958 The Vikings