On 24 July 1177, Friedrich I, Holy Roman Emperor "Barbarossa/Redbeard" Peace agreements were signed with Pope Alexander III and the Lega Lombarda/Societas Lombardorum in the northern Italian cities.
Barbarossa and Alexander III, spinello Aretino (1350–1410), Palazzo Pubblico, Siena
On 29 May 1176, after his defeat at the Battle of Legnano, Friedrich I began to seek a solution to his conflict with Pope Alexander III – nine years earlier he had crowned his supporter, a abbot named Giovanni, into the rival Pope Callixtus III.
Battle of Lenano, painted by Amos Cassioli (1832-1891).
In this document of 1177, known as the "Venice Peace Agreement", Friedrich I recognized Alexander III as pope and thus renounced support for Calixtus III. At the same time, the Redbeard King also recognized the temporal control of the city of Rome by the Apoce (although the Roman citizens were still dissatisfied and expelled Alexander III in 1179), and he also reached a six- and fifteen-year truce with the Lombard League and Guglielmo II di Sicilia in Sicily. On 25 June 1183, through the Peace Agreement of Konstanz, Barbarossa finally recognized the independence of the Lombard cities.
Venice in a manuscript of Marco Polo's travels, MS Oxford, Bodleian Library, Bodl. 264, fol. 218r
The rival Pope Kalixtus III, who was living in Viterbo at this time, was probably mentally broken. In 1178, he abandoned the struggle under the siege led by Christian I. von Buch, Archbishop of Mainz, and on August 29, 1178 surrendered to Pope Alexander III, and then... He was assigned to Benevento as chief executive.
Reference: Fortunato Olmo, an old book dedicated to this matter, "Historia della venuta à Venetia occultamente nel 1177 di papa Alessandro III e della vittoria ottenuta da Sebastiano Ziani"