Definition:Category of Monoids

Definition
The category of monoids, denoted $\mathbf{Mon}$, is the metacategory with:


 * objects: All monoids;
 * morphisms: All monoid homomorphisms.

This forms a metacategory, as shown on Category of Monoids is Category.

Note
The reason to call $\mathbf{Set}$ a metacategory is foundational; allowing it to be a category would bring us to axiomatic troubles.

Also see

 * Category of Monoid Categories