Acts 15:2

And when Paul and Barnabas had no small dissension and questioning with them, the brethren appointed that Paul and Barnabas, and certain other of them, should go up to Jerusalem unto the apostles and elders about this question.

No small dissension ... Paul would never have yielded to the Judaizing teachers, even if the whole Jerusalem church had backed them up, this being true because Paul had received a direct revelation from Jesus Christ covering the whole question. Thus, what is in view here is a very sharp clash between Paul's true position and the false position of the men who had come from Jerusalem.

The brethren appointed that Paul, etc. ... should go up ... Although it is here said that the brethren appointed Paul and company to this task, Galatians 2:2 plainly says that Paul went up "by revelation." It is no doubt true that the church did appoint them; but that is not the reason Paul went; the Lord commanded him to go.

And certain other men ... One of these was Titus (Galatians 2:1), who might have been a brother of Luke; and this would account for Titus' being nowhere mentioned in Luke's writings. This group almost certainly included the apostle Peter also; for, as Bruce said, "Peter was in residence at Antioch when the Judean emissaries arrived."[3] It was prior to their arrival however that Paul and Peter clashed over the issue so gravely threatening to disrupt Christian unity.

Should go up ... about this question ... It should be noted that Luke carefully refrained from saying that they were to go to Jerusalem to settle the question, leaving in view the fact that, through Paul's revelation, they were going up to settle the Jerusalem church on the right side of the question. The stubborn insistence of the Judean emissaries made it clear that some in the Jerusalem church intended to control the churches everywhere, compelling them to conform to their own Judaistic bias. Thus, in order to root out the heresy, that surely being what it was, it was necessary that strong action be taken against the source of it in Jerusalem.