Camera isn't following mouse in FPS

I've got the code

public class mousecam : MonoBehaviour {

 Vector2 mouseLook;

 public float sensitivity = 5.0f;
 

 GameObject character;

 void Start () 
 {
     character = this.transform.parent.gameObject;
     
 }
 

 void Update () 
 {
     var mouse = new Vector2 (Input.GetAxisRaw ("Mouse X"), Input.GetAxisRaw ("Mouse Y"));
     

     transform.localRotation = Quaternion.AngleAxis (-mouseLook.y, Vector3.right);
                                                     
     character.transform.localRotation = Quaternion.AngleAxis (mouseLook.x, character.transform.up);
                                                                 
 }

However when I play, the camera doesn't move an inch, what's going wrong?