Category of magmas
Presentation
In mathematics, let Mag the category of magma, i.e. of binary operations, with morphisms given by homomorphisms in the universal algebra sense.
Note that Set is contained in Mag as trivial [[magma (algebra) |magma]]s, with operations: right, say, projections (bad references, we need projection maps) : x T y = y. It has direct products, so the concept of a magma object (internal binary operation).
The most important property is that an injective endomorphism can be extended to an automorphism of a magma extension, just the colimit of the (constant sucesion of the) endomorphism.
Category of monoids is special, but for now redirects here.