Most organizations will give you lots of tips on how to do this when you bring your new greyhound home. Many people keep their greyhounds in crates or a dog-proofed room while they are at work. I have cats. The greyhound was bred as a hunter five thousand years ago. Some greyhounds have a keen prey drive and will chase small animals, including cats.
Some greyhounds are afraid of cats.
After a period of educating and adjusting, the vast majority of greyhounds live peaceably with cats and even sleep with them. Most organizations offers advice on helping your greyhound adjust to your small pets. I have a toddler. Greyhounds are much larger than infants, and even some youngsters up to the age of five. As with any larger dog, small children must be supervised when with a large dog.