[[Field extension]]
# Morphism of field extensions

Let $L_{1}:K$ and $L_{2}:K$ be [[Field extension|field extensions]],
with inclusions $\iota_{i} : K \to L_{i}$.
A morphism $\varphi$ from $L_{1}:K$ to $L_{2}:K$ is a morphism $\varphi : L_{1} \to L_{2}$ which fixes (the image of) $K$ pointwise, #m/def/field  i.e.
$$
\begin{align*}
\varphi \iota_{1} = \iota_{2}
\end{align*}
$$
In this way one obtains the category [[Category of field extensions]].

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#state/tidy | #lang/en | #SemBr