Your most important assets on the mountain are matches in a waterproof case and a dependable lighter. Do not fool yourself into thinking that just because the weather seems good all day that you will not have a freak snow or rainstorm. Fire makes heat. You do not want to be wet and cold on the mountain. Hypothermia can set in quickly and, YES, even in the summer months.
Fire can also keep away any unwanted visitors such as the animals of the area.
And fire of course you need to cook meals with. Fire is very important. A plastic tarp could again be a lifesaver. A tarp will provide shelter, keep you away from any nasty elements. A tarp can be used to carry your partner off the mountain in case of injury.