What are some examples of cowardice in Shakespeare's Julius Caesar?

Since the play is named after him, it is perhaps surprising that one of the most cowardly characters in Shakespeare's Julius Caesar is Caesar himself. Take, for example, lines 96-137 in Act 1, Scene 2, in which Cassius tells Brutus of several instances of Caesar's cowardice. During a swimming race, Cassius says, Caesar grew frightened and tired and had to be rescued from the water. Along the same lines, Cassius remembers an instance in which Caesar came down with a sickness and behaved pitifully: "His coward lips did from their color fly" (128), Cassius says. The implication of these two details is that, instead of acting with the courage expected of a leader, Caesar instead is ironically prone to cowardice and seems to wilt when faced with obstacles and the hardships of life. These examples are meant to undermine Caesar's status as a capable leader and suggest that he is not as fit to rule as the Roman masses think he is.