Category of medial magmas
In mathematics, the category of medial magmas, also known as the medial category, and denoted Med, is the category whose objects are medial magmas, and whose morphisms are magma homomorphisms.
The category Med has direct products, so the concept of a medial magma object makes sense. As a result, Med has all its objects as medial objects, and this characterizes it.
There is an inclusion functor from Set to Med as trivial magmas, with operations being the right projections
An injective endomorphism can be extended to an automorphism of a magma extension—the colimit of the constant sequence of the endomorphism.
