You make the call!

Batter swings and tips the ball about ten feet down the first base line and it comes to rest about six inches in fair territory. As the catcher leaves his box to field it and the batter leaves his box to advance to first, they're both within the base path, they collide and both fall to the ground. The catcher grabs the ball and tags the runner. Is the batter out or did the catcher obstruct him?