Depending on how you look at it, there are two ways to view the appearance of the ghost.
1. You could view Caesars appearance as a bad omen for Brutus.
2. You could also view it as a manifestation of Brutus' guilt for killing Caesar. He truly admired Caesar but thought that his death would make Rome a better place.
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Et Tu Brutus
If so, we are not shown it. But Caesar and Brutus had a special relationship which makes the ghost's visit to Brutus make more sense than a visit to Cassius would.
The ghost of Julius Caesar appears to Marcus Brutus in Sardis and Philippi.
The reason Antony does this is to make the citizens/ the poor to go and against Cassius, Brutus, and the conspirators. :D
He gets visited by the ghost of Caesar.