The papacy of Innocent I was all about establishing the primacy of Rome and asserting the right of the Holy See to determine orthodoxy. He took numerous actions to establish administrative control over other bishops in numerous regions and strongly supported St. Jerome and St. Augustine of Hippo. Among other things he is known for, Innocent I is credited with closing the canon of the Bible in 405 A.D. when he sent a list of sacred books to the bishop of Toulouse. This list was identical to the canon from the Council of Trent, which was held over 1,000 years later.
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From https://www.traditioninaction.org/religious/n013rp_DeathPenalty_Popes.htm :
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The first Pope to take a stand in favor of the death penalty was Innocent I in the year 405. In response to a query from the Bishop of Toulouse, Pope Innocent I based his position on Paul’s Letter to the Romans. He wrote:
It must be remembered that power was granted by God [to the magistrates], and to avenge crime by the sword was permitted. He who carries out this vengeance is God’s minister (Rm 13:1-4). Why should we condemn a practice that all hold to be permitted by God? We uphold, therefore, what has been observed until now, in order not to alter the discipline and so that we may not appear to act contrary to God’s authority.
(Innocent 1, Epist. 6, C. 3. 8, ad Exsuperium, Episcopum Tolosanum,
20 February 405, PL 20,495)