Endomorphism Semiring

The endomorphism semiring of a Commutative Monoid $M$ is a Semiring on Monoid Homomorphisms $M\to M$, where addition is given by pointwise addition, and multiplication by composition.

Properties

• Every Semiring $R$ embeds into $\mathrm{End}(R)$; this is a form of the Yoneda Embedding, and in particular Mitchell's Embedding Theorem.