Clement and Irenaeus both refer to Peters Roman ministry. His successor Linus, is mentioned by Paul and is noted to be Peters successor by Irenaeus.
Try not to get hung up on the word "Pope", it's the office that matters, not the title we use to describe it.
The commission was to open the Gospel to the JEWS, which is what we see in scripture. Paul to the gentiles and Peter to the Jews.
When Peter writes from Babylon he is writing from Rome.
Proof of that please? There is no contemporary or biblical evidence that he was ever IN Rome, but being in Babylon would have been consistent with the mission given him by God.
Just because you say it does not make it true, please show us in Scripture that Babylon DEFINITELY means Rome , and then please do not act offended if the dispensationalists say that Rome is Babylon in Revelations, you can not have it both ways
When Peter told the apostles assembled in Acts that there was no need to "..by placing on the shoulders of the disciples a yoke that neither our ancestors nor we have been able to bear? " he was preaching infallible dogma.
That was AFTER he sat in silence and gave approval for just that thing among the jews, infallible in his silence too ? It was James that spoke from the Chair of authority not peter in that counsel
And note too that no one disputed him when he said "My brothers, you are well aware that from early days God made his choice among you that through my mouth the Gentiles would hear the word of the gospel and believe." He has a particular calling and a particular authority conferred to him by Christ and recognized by the Apostles.
He is referring to Gods providence in preaching to Cornelius , that he and his house would be saved ( Vs 18). We know how hard God had to go to get him to go there don't we? Scripture is without error and from other writings we know that Peter was sent to the Jews ( as he was used on Pentecost and Paul to the gentiles) Also note the last time we read of Peter in the book of Acts. No mention of a missionary journey into the loins den of Rome, no mention of building a great church there.
He didn't need to run around telling everyone I'm the pope!", they all knew he was chosen to lead from the foundation.
Proof please .
Clement and Irenaeus both refer to Peters Roman ministry.
Clement (101 AD listed as the 4th Pope after peter, not a contemporary . Irenaeus b120/140-d200/202, also not a contemporary .
"Most reconstructions of Peter's life depend primarily on the New Testament; there are no other contemporary accounts of his life or death.
- Wikipedia, encyclopedia
He is not presented as the "pope" in Rome until the 300's . Other mentions in the century following the death of Christ ( 100-200) speak of a presence in Rome, but no mention of the status of infallible head of the Catholic Christ ( Pope)