Commutative diagrams with very round arrows?

Question

I have a diagram that has only objects in (1,1), (1,2) and (2,1). I would like an arrow that goes from (2,1) to (1.2) going around (1.1). I do succeed in curving the arrow, but not to make it round enough to avoid crossing other objects in the diagram. Here is what I have:

\documentclass{article}
\usepackage[all]{xy}
\usepackage{amscd,amssymb}

\begin{document}

\xymatrix{
p^{-1}(V)\ar[d]_p
&V\times Y\ar[l]_\varphi\ar[dl]^{\mathrm{pr}_1}\\
V\ar@/_/[u]_\sigma\ar@/^5pc/[ur]^\psi
}

\end{document}

Thanks!

Answer 1

Here's a version using tikz-cd

\documentclass[border = 5pt]{standalone}

\usepackage{tikz-cd}

\begin{document}

\begin{tikzcd}
  p^{-1}(V) 
  \arrow[d, "p"']
  & V\times Y 
  \arrow[l, "\varphi"']
  \arrow[dl, "\mathrm{pr}_1"]
  \\
  V
  \arrow[u, bend right, "\sigma"']
  \arrow[ur, rounded corners, "\psi", to path = { -- ([xshift = -4ex]\tikztostart.west) |- ([yshift = 3ex]\tikztotarget.north) [near end]\tikztonodes -- (\tikztotarget)}]
\end{tikzcd}

\end{document}