$\require{AMScd}$Are there references for a construction of the enriched slice category of $\mathcal A \in \mathcal{V}\text{-Cat}$? A reasonable definition should be

Fix an object $a\in\mathcal A$ and let the objects of ${\cal A}/a$ be the set ${\cal V}(J, {\cal A}(x,a))$ for all $x\in\cal A$. $J$ is the monoidal unit of $\cal V$.

Let ${\cal A}/a(p,q)$ be the $\cal V$-object resulting from the pullback $$ \begin{CD} P @>>> {\cal A}(x,y) \\ @VVV {}@VVq_*V\\ J @>>p> {\cal A}(x, a) \end{CD} $$ for $p : x\to a, q : y \to a$ and $J$ the monoidal unit.

Does it work for every $\cal V$?