Born in Bologna, he entered the Carthusian order in 1394, at the age of twenty. A supporter of the authority of Pope Martin V following the Western Schism, he was appointed bishop of Bologna by the latter (1417) and made his native city a center of learning.
Albergati was employed as an ambassador by several popes; in that capacity he visited France and several of the other Italian states. Notably, he represented Pope Eugene IV at the 1435 Congress of Arras. (The congress failed to make peace between England and France, but it did effect a reconciliation between Philip the Good of Burgundy and the French crown.) He was made cardinal of Santa Croce in Gerusalemme in 1426. He played a role in the Council of Basel-Ferrara-Florence and opened the Council of Florence, which brought about a short-lived union of the Latin and Greek Churches.
Among the young scholars who enjoyed were future important figures such as Popes Nicholas V and Pius II, and Francesco Filelfo. He died at Siena in 1443. Albergati was beatified on September 25, 1744.