Draw right triangular commutative diagram

Question

I was wondering how to draw the commutative diagram of the following figure. The closest I could get from previous posts is given in the code below, but it is not quite right.

\documentclass{article}
\usepackage{tikz-cd}

\begin{document}
    \[
    \begin{tikzcd}
        & X \arrow[dr,"a_i"] \\
        X|S \arrow[ur,"\pi"] \arrow[rr,"\hat{a}_i"] && R
    \end{tikzcd}
    \]
\end{document}

Answer 1

You almost had it.

Remove the & from the first row. You want the X to be in the first column above the X|S and remove one of the & in the second row.

Of course, you need to adjust the directional statements then as well.

The dr becomes d, the rr becomes r and the ur would become r.

But since you want that arrow to go from X to X|S you ought to put the \arrow[d, "\pi"] there (or \arrow[u, "\pi", leftarrow] in the X|S cell if that makes more sense from a syntactial point of view).

I've also added a ' after the "\hat{a}_i" statement so that the label is placed on the other side of the arrow. The same applied for the \pi label in case you construct the arrow from X to X|S.

---

The body of the tikzcd environment can be treated like a tabular/array where & separates the columns.

The \arrow macro starts an arrow in that cell with the target according to the directional shortcut. (Unless keys like from and to are used.)

By default, all arrows use the rightarrow style which can be inverted by using leftarrow. For more on this, I'd recommend reading the manual.

Code

\documentclass{article}
\usepackage{tikz-cd}

\begin{document}
\[
\begin{tikzcd}
    X \arrow[dr, "a_i"] \arrow[d, "\pi"']\\
    X|S \arrow[r,"\hat{a}_i"'] & R
\end{tikzcd}
\]
\end{document}

Output

Answer 2

You can consider also to use xy package that have the same structure of tikz-cd and also the same tips. See the output and the MWE.

\documentclass[a4paper,12pt]{article}
\usepackage[all,cmtip]{xy}
\begin{document}
$\xymatrix{
X\ar[dr]^{a_i}  \ar[d]_{\pi}  \\
X/S \ar[r]_{\hat{a}_i} & R}$
\end{document}

follow up

You can increase o reduce the rows @R=2cm or the columns @C=2.5cm. (2cm,2.5cm) are the measures.

\documentclass[a4paper,12pt]{article}
\usepackage[all,cmtip]{xy}
\begin{document}
$\xymatrix@R=2cm@C=2.5cm{
X\ar[dr]^{a_i}  \ar[d]_{\pi}  \\
X/S \ar[r]_{\hat{a}_i} & R}$
\end{document}