Neither one of the Catos were emperor--the first emperor is Augustus, who was born in 63, the year that Cato the Younger served as tribune-designate to counter Nepos, having served his quaestorship in 64. Famously in that year Cato swung the senate back towards Cicero's plan to execute the Catilinarians without trial, after Caesar almost successfully persuaded them just to exile the conspirators. Cato would be dead by 46, having committed suicide at Utica, well before Octavian's inheritance of Caesar's fortune in 44 and long before defeating Antony in 30.

In any case, you're asking about Cato the Elder. From Plutarch:

ἔδει δὲ ἢ πράττειν τι τῶν ἀναγκαίων οἴκοι τὸν δοῦλον ἢ καθεύδειν

But it was necessary for his slaves to either be busy with the necessities of the house, or to be asleep

But taking that out of context makes Cato seem like a much simpler person than he was. Plutarch says later in the same sentence that Cato was rather fond of sleepy slaves, which is not what you'd expect if Plutarch means that Cato was a slave-driver who didn't let his slaves rest. That's not what Plutarch means at all--he says that Cato liked sleepy slaves because they were gentler and less likely to get themselves into trouble than those that were active all the time, particularly in trouble with women