How to make a game object follow its local y-axis

Hello,

I am fairly new to Unity and I wanted to know if there was a quick way to make an object follow its local y-axis. Like

transform.forward

follows the object’s local z-axis.

i believe you are looking for transform.up

    //move up like this
    transform.position += transform.up * Time.deltaTime;
    
    //move down like this
    transform.position += -transform.up * Time.deltaTime;

        //move right  like this
    transform.position += transform.right * Time.deltaTime;
    
    //move left like this
    transform.position += -transform.right * Time.deltaTime;