IN BRIEF
The Church is apostolic. She is built on a lasting foundation: "the twelve apostles of the Lamb" (Rev 21:14). She is indestructible (cf Mt 16:18). She is upheld infallibly in the truth: Christ governs her through Peter and the other apostles, who are present in their successors, the Pope and the college of bishops.
Source: Catechism of the Catholic Church (Vatican.va)