In compiling the history of the Early Christian Church, the Liberian Catalogue (Catalogus Liberianus), which was part of the illuminated manuscript known as the Chronography of 354, is an essential document, for it consists of a list of the popes, designated bishops of Rome, ending with Pope Liberius (died 366), hence its name and approximate date. The list gives the lengths of their respective episcopates, the corresponding consular dates, and the names of the reigning emperors. In many cases there are other details. "The collection of tracts of which this forms a part was edited (apparently by one Furius Dionysius Philocalus) in 354" (CE). It now survives only in a copy.
The Liberian Catalogue is clearly the work of a compiler using earlier texts. It has been suggested that it is largely dependent on a work of Bishop Hippolytus of Portus (died 235), and is his lost Chronica. The character of the entries changes after Pontian. There are a number of "strange errors" (Edmundson 1913, lecture VIII) in the Liberian Catalogue, some of which may be the product merely of copyist errors (CE). The texts in the Chronography do display damage in transmission.
Anomalies in the Liberian Catalogue 
George Edmundson pointed out a number of anomalies. "The deaths of St. Peter and St. Paul are stated to have taken place in A.D. 55 Clement succeeds Linus in A.D. 67, and Anencletus, the real successor of Linus, is duplicated and follows Clement, first at Cletus, then as Anacletus. Clement’s death is recorded as having occurred sixteen years before he became bishop according to the generally received date." Nor were the errors confined to the first-century episcopates. The Hippolytean source is not even accurate about Pope Pius himself, who in the words of the Muratorian fragment lived "very recently in our own times". Hegesippus and Irenaeus, both of whom stayed some time in Rome soon after the death of Pius, both give the order of succession as Pius, Anicetus, Soter, Eleutherus. The Liberian Catalogue makes Pius the successor of Anicetus instead of the predecessor.
"Depositio martyrum" and the "Depositio episcoporum" 
Two other lists are associated, in the sense that they occur in the same manuscript (the Chronographus anni 354). These are the Depositio martyrum and Depositio episcoporum. While these names could be generic, for lists of martyrs and bishops, scholarly usage without qualification tends to mean these lists.
See also 
- George Edmundson, 1913. The Church in Rome in the First Century (Bampton Lectures) (Lecture VIII, on-line)
- Catholic Encyclopedia: "Chronological Lists of Popes" (on-line)