How to create up arrow with two heads?

Question

With \twoheadrightarrow we can get arrow with two heads. Is there any command for getting two heads with up arrow?

Answer 1

One can rotate one of the existing two-headed arrows (some adjustment might be required depending on the desired position for the arrow baseline):

\documentclass{article}
\usepackage{amssymb}
\usepackage{graphicx}

\newcommand\twoheaduparrow{\mathrel{\rotatebox{90}{$\twoheadrightarrow$}}}

\begin{document}

\[
A\twoheadrightarrow B\quad A\twoheaduparrow B
\]

\end{document}

Adding [origin=<origin>] as an option to \rotate, the center for rotation can be changed (possible values for <origin> are t (top),b (bottom),l (left),r (right),c (center), and B (baseline)):

\documentclass{article}
\usepackage{amssymb}
\usepackage{graphicx}

\newcommand\twoheaduparrow{\mathrel{\rotatebox[origin=c]{90}{$\twoheadrightarrow$}}}

\begin{document}

\[
A\twoheadrightarrow B\quad A\twoheaduparrow B
\]

\end{document}

In a comment it has been requested a definition without using additional packages; in this case, with a little more work, one can build the symbol using \ooalign and two shifted \uparrows:

\documentclass{article}

\makeatletter
\newcommand\twoheaduparrow{%
\mathrel{\mathchoice
  {\raise2pt\hbox{%
  \ooalign{\hss$\uparrow$\hss\cr\lower2pt\hbox{%
  $\uparrow$}}}}
  {\raise2pt\hbox{%
  \ooalign{\hss$\uparrow$\hss\cr\lower2pt\hbox{%
  $\uparrow$}}}}
  {\raise1.5pt\hbox{%
  \ooalign{\hss$\scriptstyle\uparrow$\hss\cr\lower1.5pt\hbox{%
  $\scriptstyle\uparrow$}}}}
  {\raise1.1pt\hbox{%
  \ooalign{\hss$\scriptscriptstyle\uparrow$\hss\cr\lower1.1pt\hbox{%
  $\scriptscriptstyle\uparrow$}}}}
}}

\begin{document}

\[
A\twoheaduparrow B\quad {\textstyle A\twoheaduparrow B}\quad A_{A\twoheaduparrow B}\quad L_{A_{A\twoheaduparrow B}}
\]

\[
A\uparrow B\quad {\textstyle A\uparrow B}\quad A_{A\uparrow B}\quad L_{A_{A\uparrow B}}
\]

\end{document}

Answer 2

The gap between arrow heads is set at .3\arrowheight and can be changed. Of note in this solution is the \ThisStyle{...\SavedStyle...} construct which allows the current (at invocation) math style to be imported into places where it would otherwise be lost.

That feature allows a four-pronged \mathchoice to be replaced with a single \ThisStyle{} (of course, the \mathchoice resides within \ThisStyle, but it sure saves on typing). And because I defined the arrow gap (.3\arrowheight) in terms of the length of the current mathstyle arrow, I didn't need to apply different stackgaps (i.e., arrowhead shift lengths) for each mathstyle. Furthermore, using the arrow height itself to define the magnitude of the shift means that this solution works just fine if presented in \Huge. Other solutions will not hold up so well.

As a final note, this solution preserves the baseline of the original \uparrow, which a rotated-arrow solution will not do without further manipulation.

\documentclass{minimal}
\usepackage{scalerel}
\usepackage{stackengine}
\newlength\arrowheight
\newcommand\doubleuparrow{%
  \mathrel{\ThisStyle{%
    \setlength{\arrowheight}{\heightof{$\SavedStyle\uparrow$}}%
    \stackengine{.3\arrowheight}{$\SavedStyle\uparrow$}%
      {$\SavedStyle\uparrow$}{O}{c}{F}{F}{L}}
}}
\begin{document}
\begin{equation}
A \doubleuparrow C \quad A_{A \doubleuparrow C}
\end{equation}
\end{document}

SUPPLEMENT

A commenter asks if the vertical size can be made to match the normal \uparrow. One could clip the bottom. However, here, I choose to scale down the result to the same height as the \uparrow.

\documentclass{minimal}
\usepackage{scalerel}
\usepackage{stackengine}
\newlength\arrowheight
\newcommand\doubleuparrow{%
  \mathrel{\ThisStyle{%
    \setlength{\arrowheight}{\heightof{$\SavedStyle\uparrow$}}%
    \scalerel*{\stackengine{.3\arrowheight}{$\SavedStyle\uparrow$}%
      {$\SavedStyle\uparrow$}{O}{c}{F}{F}{L}}{\uparrow}}
}}
\begin{document}
\begin{equation}
A \uparrow \doubleuparrow C \quad A_{A \uparrow \doubleuparrow C}
\end{equation}
\end{document}

If one would prefer a stretch to a scale, just substitute \stretchrel for \scalerel, to get