Definition: Let $(\mathcal C,U)$ be a concrete category over $\mathcal B$. A morphism $f: x\to y$ in $\mathcal C$ is called $\textbf{initial}$ if for any object $c\in \mathcal C$, a morphism $g:U(c)\to U(x)$ is a morphism in $\mathcal{C}$ whenever $f\circ g: U(c)\to U(y)$ is a morphism in $\mathcal C$.
Definition: An initial morphism $f:x\to y$ such that the underlying morphism $U(f):U(x)\to U(y)$ is monic is called an $\textbf{embedding}$.
Definition: If $f:x\to y$ is an embedding, then $(x, f)$ is called an $\textbf{initial subobject}$ of $y$.
Definition: In a concrete category an object $I$ is called $\textbf{injective}$ provided that for any embedding $m: A \to B$ and any morphism $f: A\to C$ there exists a morphism $g:B\to C$ extending $f$, i.e., $g\circ m=f$
Definition: A concrete category $\textbf{has enough injectives}$ provided that each of its objects is an initial subobject of an injective object.
Theorem: The category $\mathcal{T}\mathrm{op}^{CH}$ of compact Hausdorff space has enough injectives.