In Catholicism, a dogmatic definition is an infallible statement published by a pope or an ecumenical council concerning a matter of faith or morals, the belief in which the Catholic Church requires of all Christians (although Christians who are not Catholic do not recognize the Catholic Church's authority in such matters).
Contrary to the stereotype that Catholics think that everything that the pope says is infallible (or that the pope is impeccable, unable to sin), dogmatic definitions by popes are in fact very rare. Among them are Ineffabilis Deus, the definition by Pope Pius IX in 1854 concerning the Immaculate Conception of Mary, and Munificentissimus Deus, the definition by Pope Pius XII in 1950 concerning the Assumption of Mary.

Infallibility in non-Catholic churches
See infallibility of the Church for an account of the way in which not only Catholic, but also Eastern Orthodox and other churches understand this concept.