Solution
= Solution
The <comma category> $(X\downarrow G)$ has objects $(A,x)$ with $A\in\mathcal C$ and a <function> $x:X\to GA$. A <morphism> $(A,x)\to(B,y)$ is an arrow $f:A\to B$ such that $Gf\,x=y$. Identities and composition come from $\mathcal C$. When $X=1$, a map $1\to GA$ selects an element of $GA$, so this is the covariant <category of elements> of $G$.