Every group is naturally isomorphic to its opposite group via the inverse map
In other words, products are taken with order reversed. Then, is isomorphic to the opposite group via the map .
This isomorphism is natural in the sense that it gives a natural isomorphism between the identity functor and the functor sending each group to its opposite group.
- Inverse map is involutive: This states that for all in a group, and for all in a group.