How do I branch arrows using Tikz?

Question

I am drawing a diagram with nodes and arrows using Tikz, but do not have an idea how I can make an arrow branch into two.

I am using something very similar to this:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}
  \matrix (m) [matrix of math nodes,row sep=3em,column sep=4em,minimum
    width=2em]
  {
     F_t(x) & F(x) \\
     A_t & A \\};
  \path[-stealth]
    (m-1-1) edge node [left] {$\mathcal{B}_X$} (m-2-1)
        edge [double] node [below] {$\mathcal{B}_t$} (m-1-2)
    (m-2-1.east|-m-2-2) edge node [below] {$\mathcal{B}_T$}
            node [above] {$\exists$} (m-2-2)
    (m-1-2) edge node [right] {$\mathcal{B}_T$} (m-2-2)
            edge [dashed,-] (m-2-1);
\end{tikzpicture}
\end{document}

Code reference

Answer 1

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.