\documentclass{amsart}
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage{geometry,mathtools}
\geometry{a4paper}

\begin{document}

$A \underset{\psi \circ \psi \circ \psi \circ \psi}{\overset{\varphi \circ
\varphi \circ \varphi \circ
\varphi}{\mathrel{\substack{\longrightarrow\\[-0.6ex]\longleftarrow}}}} A$

\end{document}
