= Solution
The <comma category> $(X\downarrow G)$ has objects $(A,x)$ with $A\in\mathcal C$ and a <function> $x:X\to G(A)$. Its <morphisms> $(A,x)\to(B,y)$ are maps $f:A\to B$ in $\mathcal C$ satisfying $G(f)x=y$. The <identity morphism> and <composition in a category> are inherited from $\mathcal C$; the <functor> laws make the defining equations stable under both.
For a singleton $1$, its map $1\to G(A)$ is just an element $a\in G(A)$. Thus $(1\downarrow G)$ is the covariant <category of elements> of $G$, with arrows $f:(A,a)\to(B,b)$ satisfying $G(f)(a)=b$.
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