xymatrix and cartesian product

Question

I am using this to produce a diagram

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[all]{xy}
\begin{document}
[
\xymatrix{H_n(X;R) \ar[d]^{f_}&  \times  & H^m(X;R) \ar[r] & H_{n-m}(X;R) \ar[d]^{f_} \
H_n(X;R)&  \times  & H^m(X;R)\ar[u]{f^*} \ar[r]  &H{n-m}(Y;R)}
]
\end{document}

because I want an arrow between each component of the product. How can I suppress the space on each side of \times ?

That said, I don't think xy can do that. You can with tikzcd (which I'd recommend over xy nowadays, more features, nicer arrows). But it would probably just be easier to x shift the arrows instead. AFAIR xy can do this as well. — daleif, Jun 29 '20 at 12:36

daleif · Accepted Answer · 2020-06-29T12:51:28.203

I don't think xy can do what you ask, but tikz-cd can. Though I'd probably just use the xshift solution (second tikzcd example).

The xy equivalent for xshift can be seen in section 2.4 in the xy manual (xyguide.pdf)

\documentclass[a4paper]{article}
\usepackage{amsmath,amssymb}
\usepackage[all]{xy}
\usepackage{tikz-cd}
\usetikzlibrary{babel} % if you are using a language that makes " an active char
\begin{document}
Standard xy:
[
\xymatrix{H_n(X;R) \ar[d]^{f_}&  \times  & H^m(X;R) \ar[r] & H_{n-m}(X;R) \ar[d]^{f_} \
H_n(X;R)&  \times  & H^m(X;R)\ar[u]{f^*} \ar[r]  &H{n-m}(Y;R)}
]
Tikzcd with column space adjustment:
[
  \begin{tikzcd}
    H_n(X;R) \arrow[d,"f_*"] &[-3em]  \times  &[-3em] H^m(X;R) \arrow[r] &  H_{n-m}(X;R) \arrow[d, "f_*"]
    \
    H_n(X;R)&  \times  & H^m(X;R)\arrow[u,"f^*"] \ar[r]  &H_{n-m}(Y;R)\
\end{tikzcd}
]
Tikzcd using xshift instead:
[
  \begin{tikzcd}
    H_n(X;R)    \times   H^m(X;R) \arrow[d,"f_*",xshift=-2em]  \arrow[r] &  H_{n-m}(X;R) \arrow[d, "f_*"]
    \
    H_n(X;R)  \times   H^m(X;R)\arrow[u,"f^*",xshift=2em] \ar[r]  &H_{n-m}(Y;R)\
\end{tikzcd}
]
\end{document}

egreg · Answer 2 · 2020-06-29T12:58:24.650

You can slide arrows; use the amount you think best.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[all,cmtip]{xy}
\begin{document}
[
\xymatrix{H_n(X;R) \times H^m(X;R) \ar@<-2.5em>[d]{f} \ar[r] & H_{n-m}(X;R) \ar[d]^{f_} \
H_n(X;R) \times H^m(X;R) \ar@<-2.5em>[u]{f^*} \ar[r] & H{n-m}(Y;R)}
]
\end{document}

Without “thumb computation”:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[all,cmtip]{xy}
\newlength{\shiftA}
\newlength{\shiftB}
\begin{document}
[
\settowidth{\dimen0}{$H_n(X;R)$}
\settowidth{\dimen2}{$H^m(X;R)$}
\settowidth{\dimen4}{${}\times{}$}
\setlength{\shiftA}{\dimexpr(\dimen0+\dimen4)/2}
\setlength{\shiftB}{\dimexpr(\dimen2+\dimen4)/2}
\xymatrix{H_n(X;R) \times H^m(X;R) \ar@<-\shiftA>[d]{f} \ar[r] & H_{n-m}(X;R) \ar[d]^{f_} \
H_n(X;R) \times H^m(X;R) \ar@<-\shiftB>[u]{f^*} \ar[r] & H{n-m}(Y;R)}
]
\end{document}

xymatrix and cartesian product

2 Answers2