\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
  \node (A) at (0, 3) {$ \mathbb{F}^{n} $};
  \node (B) at (4, 3) {$ \mathbb{F}^{n} $};
  \node (C) at (0, 1.5) {$ \operatorname{span}\{x_{1}, \dots, x_{n}\} $};
  \node (D) at (4, 1.5) {$ \operatorname{span}\{x_{1}, \dots, x_{n}\} $};
  \node (E) at (0, 0) {$ \mathbb{F}[x_{1}, \dots, x_{n}, \dots] $};
  \node (F) at (4, 0) {$ \mathbb{F}[x_{1}, \dots, x_{n}, \dots] $};
  \draw[-latex] (A) -- node[above] {$ \rho_{x} $} (B);
  \draw[latex-latex] (A) -- node[left] {$ \varphi $} (C);
  \draw[latex-latex] (B) -- node[right] {$ \varphi $} (D);
  \draw[-latex] (C) -- node[above] {$ \widetilde{\rho_{x}} $} (D);
  \draw[-latex] (E) -- node[above] {$ \widetilde{\rho_{x}} $} (F);
  \draw[-latex] (2, 1.2) -- node[right] {extend} (2, .7);
\end{tikzpicture}
\end{document}