Equivalent of `@VVV` for uparrow in commutative diagram?

Question

Following questions like this, I managed to draw a commutative diagram like below using package AMScd:

$$\require{AMScd}\begin{CD} X @>>> X \\ @V{f}VV @V{f^{-1}}VV \uparrow \\ X @>>> X \\ \end{CD}$$

$$\require{AMScd}\begin{CD}
X @>>> X \\
@V{f}VV @V{f^{-1}}VV \uparrow \\
X @>>> X \\
\end{CD}$$

However, none of the answers shows an arrow that's vertically up, and \uparrow is to short (see diagram). So what's the analog of @VVV for upwards pointing arrow? @VVV is particularly nice because you can add labels at different positions.

Answer 1

Using A rather than V (or AAA rather than VVV) seems to be working:

$$\require{AMScd}\begin{CD}
X @>>> X \\
@A{f}AA @A{f^{-1}}AA  \\
X @>>> X \\
\end{CD}$$

$$\require{AMScd}\begin{CD} X @>>> X \\ @A{f}AA @A{f^{-1}}AA \\ X @>>> X \\ \end{CD}$$

I will mention that the syntax here should be the same (or at least similar) as in the amscd package. The documentation for this package can be found in various places.