My friend, I warmly suggest you the usage of tikzcd
package. It truly makes life easier. You can find an exhaustive documentation here. And now onto the code. You'll see It's much shorter than the average painful tikz
source:
\documentclass[a4paper]{report}
\usepackage{amsmath}
\usepackage{tikz-cd}
\begin{document}
\[
\begin{tikzcd}[column sep=large, row sep=large]
F_t(x) \arrow[d, "\mathcal{B}_X"'] \arrow[r, "\mathcal{B}_t"', rightharpoondown, shift right=0.25ex] \arrow[r, rightharpoonup, shift left=0.25ex] & F(x) \arrow[d, "\mathcal{B}_T"] \\
A_t \arrow[ru, dashrightarrow, dash] \arrow[r, "\exists", "\mathcal{B}_T"'] & A
\end{tikzcd}
\]
\end{document}

Or if you perhaps want two normal arrows pointing in the same direction:
\documentclass[a4paper]{report}
\usepackage{amsmath}
\usepackage{tikz-cd}
\begin{document}
\[
\begin{tikzcd}[column sep=large, row sep=large]
F_t(x) \arrow[d, "\mathcal{B}_X"'] \arrow[r, "\mathcal{B}_t"', shift right=0.65ex] \arrow[r, shift left=0.65ex] & F(x) \arrow[d, "\mathcal{B}_T"] \\
A_t \arrow[ru, dashrightarrow, dash] \arrow[r, "\exists", "\mathcal{B}_T"'] & A
\end{tikzcd}
\]
\end{document}

I'd be impolite if I didn't answer your question specifically. Perhaps you are very skilled in tikz
and don't feel like jumping onto another package. I understand. Though I have to warn you that path
is not the best way to go about. In fact (for commutative diagrams) it's pretty horrible. I rewrote the whole diagram because I wasn't able to find a solution in path
environment. It kind of castrates a wide portion of functions tikz
has to offer, like for example xshift
and yshift
I used to move the arrows. Here's a solution in plain tikz
:
\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[node distance=2.3cm, auto]
\node (A) {$F_t(x)$};
\node(B) [right of=A] {$F(x)$};
\node (C) [below of=A] {$A_t$};
\node (D) [right of=C] {$A$};
\draw[transform canvas={yshift=0.5ex},->] (A) -- (B);
\draw[transform canvas={yshift=-0.5ex},->](A) to node [below] {$\mathcal{B}_{t}$} (B);
\draw[->](A) to node [left] {$\mathcal{B}_{X}$}(C);
\draw[->](B) to node {$\mathcal{B}_{T}$}(D);
\draw[->](C) to node [below] {$\mathcal{B}_{T}$}(D);
\draw[](C) to node [above] {$\exists$}(D);
\draw[dashed](B) to (C);
\end{tikzpicture}
\end{document}

I hope this post was helpful to you. I wish you a good day.
edge
gets its own arrow tip, because that's howedge
s work. You can use regular path construction commands between nodes if you just want a tip at the end, say.\draw [->] (0,0) to[bend left] (-1,-2); \draw [->] (0,0) to[bend right] (1,-2);
?