Get cleveref type, only

Question

I am using the xr and cleveref packages to reference figures in another document, using the same figure and table numbers as the other document, as shown here. However, for non-floating figures and tables, I can't use the \@captype used in \extref. Therefore, I'd like to get the cleveref type of a given reference. However, I have been unable to find a technique for this.

Here's a MWE without xr and the external document (because I don't think those complications are important for this question, unless there's no way to extract the cleveref type).

Updated MWE (showing more precisely the problem):

\documentclass{article}
\usepackage{graphicx}
\usepackage{cleveref}
\usepackage{caption}
\makeatletter
\newcommand{\extref}[1]{%
  @namedef{the@captype}{\ref{#1}}%
}
\makeatother
\begin{document}
\begin{center}
\includegraphics{example-image-a.jpg}
\captionof{figure}{caption\label{fig:example}}
\end{center}
\begin{center}
\includegraphics{example-image-a.jpg}
\extref{fig:example}
\captionof{figure}{repeated}
\end{center}
Here is a reference: \cref{fig:example}.
\end{document}

Answer 1

That's what \namecref is for:

\documentclass{article}
\usepackage{graphicx}
\usepackage{cleveref}
\begin{document}
\begin{figure}
\includegraphics{example-image-a.jpg}
\caption{caption\label{fig:example}}
\end{figure}
Here is a reference: \cref{fig:example}.
Now I want to know the label type: \namecref{fig:example}
\end{document}

Edit: Getting the type proper, instead of the type name, as requested in the comments:

\documentclass{article}
\usepackage{graphicx}
\usepackage{cleveref}
\makeatletter
\newcommand{\mycreftype}[1]{%
  \cref@gettype{#1}{@mytempvar}%
  @mytempvar}
\makeatother
\begin{document}
\begin{figure}
\includegraphics[width=\linewidth]{example-image-a.jpg}
\caption{caption\label{fig:example}}
\end{figure}
Here is a reference: \cref{fig:example}.
Now I want to know the label type: \mycreftype{fig:example}
\end{document}