James head of the early church?

In Galatians, Paul referred to James as the Lord's brother and as seeming to be a pillar of the Jerusalem church, along with Peter and John. Of the three, it is hard to prove whom he saw as the leader, but one clue is that when he speaks of all three, he mentions James first. Paul also seems to treat Peter as an equal, suggesting either that he did not regard the leader of the Jerusalem church as the leader of all Christianity, or that Peter was not the leader of the Jerusalem church and James or John was. Thus it seems somewhat likely that James was the leader of Jesus' followers, at least in Jerusalem.