# Very curved arrow with tikzcd

Problem

I would like the arrow in the diagram

to extend farther to the right, so that it doesn't overlap with the long formula I have in the middle.

Current code

I am using the bend right option:

  \begin{equation*}
\begin{tikzcd}
A
&
\\
BBBBBBBBB \ar{u}
&
\\
C \ar{u}\ar[uu,"f^*",bend right=90,swap]
&
\end{tikzcd}
\end{equation*}


Attempted solution

I attempted to use a control:

  \begin{equation*}
\begin{tikzcd}
A
&
\\
BBBBBBBBB \ar{u}
&
\\
C \ar{u}\ar[uu,"f^*",to path={..controls +(2.5,1.5) .. (\tikztotarget)},swap]
&
\end{tikzcd}
\end{equation*}


This produces a diagram that looks like:

It's not overlapping anymore, but it doesn't look great, and more importantly the label $f^*$ disappeared.

above image exploit option looseness from TikZ:
\documentclass[border=3mm,
$\begin{tikzcd} A & \\ BBBBBBBBB \ar{u} & \\ C \ar{u}\ar[uu,"f^*",bend right=90,looseness=2,swap] & \end{tikzcd}$