What is the Pope's cathedral church called?

The pope does not live in a 'palace.' He normally lives in the Papal Apartments on St. Peter's Square and they are fairly simple in their furnishings. The apartments are in the Apostolic Palace. However, Pope Francis has chosen to stay in a simple apartment in the Casa Santa Marta, a hospice in the Vatican meant to house cardinals during a conclave or for the use of dignitaries visiting on official business.