\begin{definition}[Definition:Polynomial Evaluation Homomorphism/Single Indeterminate]
Let $R, S$ be commutative rings with unity.
Let $\kappa: R \to S$ be a unital ring homomorphism.
Let $\struct {R \sqbrk X, \iota, X}$ be a polynomial ring in one variable over $R$.
Let $s\in S$.
A ring homomorphism $h : R \sqbrk X \to S$ is called an '''evaluation in $s$''' {{iff}}:
:$\map h X = s$
:$h \circ \iota = \kappa$
where $\circ$ denotes composition of mappings.
\end{definition}