What was the relationship between Pontius Pilate and Caiaphas?
At dawn they led Jesus from the house of Caiaphas to the praetorium. Pilate came out to ask what they accused him of. John 18:28-29
What the Bible says
John 18:28
Then they led Jesus from Caiphas to the governor’s hall. And it was morning; and they went not into the hall, that they might not be defiled, but that they might eat the pasch.
John 18:29
Pilate therefore went out to them, and said: What accusation bring you against this man?
Douay-Rheims Bible (Challoner revision), public domain.
What the Church teaches
The Catechism explains that the Sanhedrin, which had no power to condemn anyone to death, handed Jesus over to the Romans.
Catechism 596 · Catechism of the Catholic Church
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Meet Pontius Pilate and Caiaphas.