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This is a natural transformation of binary operation from a group to its opposite. ⟨g₁, g₂⟩ denotes the ordered pair of the two group elements. *' can be viewed as the naturally induced addition of +.

In group theory, a branch of mathematics, an opposite group is a way to construct a group from another group that allows one to define right action as a special case of left action.

Monoids, groups, rings, and algebras can be viewed as categories with a single object. The construction of the opposite category generalizes the opposite group, opposite ring, etc.