  We show that 2-categories of the form $\mathscr{B}\mbox{-}\mathbf{Cat}$ are
closed under slicing, provided that we allow $\mathscr{B}$ to range over
bicategories (rather than, say, monoidal categories). That is, for any
$\mathscr{B}$-category $\mathbb{X}$, we define a bicategory
$\mathscr{B}/\mathbb{X}$ such that
$\mathscr{B}\mbox{-}\mathbf{Cat}/\mathbb{X}\cong
(\mathscr{B}/\mathbb{X})\mbox{-}\mathbf{Cat}$. The bicategory
$\mathscr{B}/\mathbb{X}$ is characterized as the oplax limit of $\mathbb{X}$,
regarded as a lax functor from a chaotic category to $\mathscr{B}$, in the
2-category $\mathbf{BICAT}$ of bicategories, lax functors and icons. We prove
this conceptually, through limit-preservation properties of the 2-functor
$\mathbf{BICAT}\to 2\mbox{-}\mathbf{CAT}$ which maps each bicategory
$\mathscr{B}$ to the 2-category $\mathscr{B}\mbox{-}\mathbf{Cat}$. When
$\mathscr{B}$ satisfies a mild local completeness condition, we also show that
the isomorphism $\mathscr{B}\mbox{-}\mathbf{Cat}/\mathbb{X}\cong
(\mathscr{B}/\mathbb{X})\mbox{-}\mathbf{Cat}$ restricts to a correspondence
between fibrations in $\mathscr{B}\mbox{-}\mathbf{Cat}$ over $\mathbb{X}$ on
the one hand, and $\mathscr{B}/\mathbb{X}$-categories admitting certain powers
on the other.
