Triangular commutative diagram

Question

I am using the \xymatrix command

this is the code I've written

\[\xymatrix{
& A \ar[d]^{i}\\
 B \ar@{-->}[ru]^-{\exists \overset{\sim} \varphi}\ar[r]^{\varphi}&C
}\]

My problem is with the [ru]... The dashed arrow goes upward, whereas I want it to go downward; and I keep getting an error !

Answer 1

You could use \ar@{<--}, but it's conceptually better to originate it from A:

\documentclass{article}
\usepackage{amsmath}
\usepackage[all,cmtip]{xy}

\begin{document}

\[
\xymatrix{
  & A \ar[d]^{i} \ar@{-->}[dl]_-{\exists \tilde{\varphi}} \\
  B \ar[r]^{\varphi} &C
}
\]

\end{document}

Note \tilde{\varphi}, rather than \overset{\sim}{\varphi}. You can use \widetilde if the accent seems too short.

Alternatively, you can use tikz-cd

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

\begin{document}

\[
\begin{tikzcd}
  {} & A \arrow{d}{i} \arrow[dashed,swap]{dl}{\exists \tilde{\varphi}} \\
  B \arrow{r}{\varphi} & C
\end{tikzcd}
\]

\end{document}