Definition:Initial Homomorphism from Integers to Ring with Unity

Definition
Let $\Z$ be the ring of integers.

Let $R$ be a ring with unity.

The initial homomorphism $\Z \to R$ is the unital ring homomorphism that sends $n \in \Z$ to the $n$th power of $1$ in $R$:
 * $ n \mapsto n \cdot 1$.

Also see

 * Initial Homomorphism from Integers is Ring Homomorphism
 * Ring of Integers is Initial Object in Category of Rings with unity