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The aura (background) is a trait but its not equipment. It represents the category of the Gainling. Each aura has its strength and weakness against other auras. For example the 'Aqua' aura is weak against 'Wizards' and strong against 'Blood'. A strength against another Gainling means you pierce the armor of this Gainling. Consequently its defense points will not be included into the calculation of the battle.
These rules apply on all battles and Gainlings, no matter who attacks/defends.