xymatrix arrow changing directions

In an \xymatrix environment, how can I get an arrow going down, then two steps right and then up again, as in the picture? In the good old days there was LAMSTeX to do this kind of things, but not anymore. From the XYPic manual I realize that I have to use the grave accent to type directions but I couldn't figure out how, and furthermore arrows displayed in that manual are bending and not changing direction at straight angles.

Not a direct answer to your question, but tikz-cd is much better than Xy-pic.

With some help from the manuals and a bit of luck…

\documentclass{article}
\usepackage{amsmath,amssymb,tikz-cd,eucal}

\DeclareMathOperator{\ind}{ind}

\begin{document}

$\begin{tikzcd}[column sep=large] V_m \arrow[r,"\iota"] \arrow[rr,"{\phi_{m+b,m}}", to path = { -- ++(0,-2em) -| (\tikztotarget)[near start]\tikztonodes }, ] & \ind_{\mathcal{S}_m\times\mathcal{S}_b}^{\mathcal{S}_{m+b}}(V_m\boxtimes\mathcal{A}_b) \arrow[r,"{\Phi_{m+b,m}}"] & V_{m+b} \end{tikzcd}$

\end{document} I found the solution with bending angles:

\ar d[d] [rr]^-{\phi_{m+b,m}}  [rr]

Could someone please explain how it works?

Why is there a d outside the brackets and then one inside the brackets?

Why is there no r outside the brackets for the second segment?

How does xy know at what angle to finish the arrow if there is no third segment?

Is there a solution with sharp angles?

Surely there is a lot of work to build with xy package your image...In fact I have used near one hour :-(...I'm not as the light ....and I think that xy package not have the square but curved arrow that connect two elements of a matrix.

\documentclass[a4paper,12pt]{article}
\usepackage[all,cmtip]{xy}
\usepackage{mathtools,amssymb,eucal}
\usepackage{scalerel}

\begin{document}
$\xymatrix@C=4pc{% V_m \vphantom{\scaleobj{2.5}{\frac AB}}\ar[r]^{\mkern-80mu\iota} \ar@<-1pt> d/5pt[r] [rr]^{\phi_{m+b,m}} [rr] & \text{Ind}^{\mathcal{S}_{m+b}}_{\mathcal{S}_{m}\times \mathcal{S}_{b}}(V_m \boxtimes \mathcal{A}_b) \ar[r]^{\mkern50mu\mathit{\Phi}_{m+b,m}} & V_{m+b} }$
\end{document} 