(Total and Surjective) Relation - arrows

Question

I am looking for following symbols:

Total Relation: <<->
Surjective Relation: <->>
Total surjective Relation: <<->>

This is the sort of thing I’m looking for (source):

Can anybody help me?

Thanks in advance.

Answer 1

Here's a way to build symbols like in the document you link to:

\documentclass{article}
\usepackage{mathtools}

\newcommand{\negjoinrel}{\mathrel{\mkern3mu}}
\newcommand{\rlaprel}[1]{\mathrel{\mathrlap{#1}}}
\newcommand{\rel}{\rlaprel{\leftarrow}\negjoinrel\rightarrow}
\newcommand{\trel}{\rlaprel{\leftarrow}\negjoinrel\rlaprel{\leftarrow}\rightarrow}
\newcommand{\srel}{\rlaprel{\leftarrow}\rlaprel{\rightarrow}\negjoinrel\rightarrow}
\newcommand{\tsrel}{\rlaprel{\leftarrow}\negjoinrel\rlaprel{\leftarrow}
                    \joinrel\rlaprel{\rightarrow}\negjoinrel\rightarrow}


\begin{document}
\noindent
$A\rel B\trel C\srel D\tsrel E$

\noindent$\rel$\\$\trel$\\$\srel$\\$\tsrel$
\end{document}

You can see that they all have the same width.

Answer 2

Is this what you want?

$\ll \gg$ 

Or this (from amssymb):

$\twoheadleftarrow \twoheadrightarrow \rightarrowtail \leftarrowtail$