Auto magma object

In mathematics, a magma object, can be defined in any category formula_1 equipped with a distinguished bifunctor formula_2. Since Mag, the category of magmas, has cartesian products, we can therefore consider magma objects in the category Mag. These are called auto magma objects. There is a more direct definition: an auto magma object is a set formula_3 together with a pair of binary operations formula_4 satisfying formula_5 for all formula_6 in formula_3. A medial magma is the special case where these operations are equal.