2 Indeed the unique gift of Peter's primacy is that he might spread everywhere and preserve the riches of charity and faith, as Ignatius Theophorus, a man of Apostolic times, beautifully declared. For in those noble letters he wrote to the Roman Church on his journey, announcing his arrival in Rome to be martyred for Christ, he gave testimony to the primacy of that Church over all others by calling it 'presiding officer over the universal community of charity." This was to signify not only that the Universal Church was the visible image of divine charity, but also that Blessed Peter, together with his primacy and his love for Christ (affirmed by his triple confession), remains heir of the Roman See. Accordingly the souls of all the faithful should be ignited by the same fire.
Source: Principi Apostolorum Petro (Vatican.va)