misdirected xymatrix arrow heads with certain fonts

Question

I'd like to use $\mathsf{C}$ rather than $\mathcal{C}$ for categories. However, when I use the former in the first displayed equation, the top arrowhead (the arrow labelled L) points northwest, rather than southwest, as you'd expect. In the second displayed equation, with the wrong font, this arrow points in the correct direction. If I unload all the packages except xy, the problem disappears.

Any idea what's going on?

\documentclass{amsbook}
\usepackage{amsfonts, amsmath, amssymb}
\usepackage{stmaryrd}
\usepackage{txfonts} 
\usepackage{comment}
\usepackage{enumitem}
\usepackage{epigraph}
\usepackage{dialogue}
\usepackage{xcolor}
\usepackage{graphicx}

\usepackage{amsmidx}%for the index
\makeindex{idx}
\makeindex{nidx}%index of notation
\makeindex{cidx}%index of categories
\newcommand{\idx}{\index{idx}}
\newcommand{\nidx}{\index{nidx}}
\newcommand{\cidx}{\index{cidx}}

\usepackage[pdfborder=0, hidelinks]{hyperref}

\usepackage[all,pdftex]{xy}
\newdir{ >}{{}*!/-10pt/@{>}}

\begin{document}

$$\xymatrix{ \mathsf{C} \ar[r]|U & \mathsf{D} \ar@{->}@/_3ex/[l]_L^\perp \ar@/^3ex/[l]^R_{\perp} }$$
$$\xymatrix{ \mathcal{C} \ar[r]|U & \mathsf{D} \ar@{->}@/_3ex/[l]_L^\perp \ar@/^3ex/[l]^R_{\perp} }$$

\end{document}

Answer 1

I can reproduce the issue with this minimal example:

\documentclass{amsbook}
\usepackage{txfonts}
\usepackage[all]{xy}
\newdir{ >}{{}*!/-10pt/@{>}}

\begin{document}

\[
\xymatrix{
  \mathsf{C} \ar[r]|U & \mathsf{D} \ar@{->}@/_3ex/[l]_L^\perp \ar@/^3ex/[l]^R_{\perp}
}
\]

\[
\xymatrix{
  \mathcal{C} \ar[r]|U & \mathcal{D} \ar@{->}@/_3ex/[l]_L^\perp \ar@/^3ex/[l]^R_{\perp}
}
\]

\end{document}

Note that you shouldn't pass the pdftex option (but it's not relevant to the issue).

If I change \usepackage{txfonts} into \usepackage{newtxtext,newtxmath}, the problem disappears:

The NewTX fonts are an edited version of TXfonts, fixing the (many) misfeatures of the latter, especially with regards to spacing.

You might want to look at tikz-cd (it works also with txfonts, but I don't recommend it).

\documentclass{amsbook}
\usepackage{newtxtext,newtxmath}
\usepackage{tikz-cd}

\begin{document}

\[
\begin{tikzcd}[column sep=3em]
\mathsf{C} \arrow[r,"U" description] &
  \mathsf{D}
  \arrow[l,bend right=50,"\perp","L" swap]
  \arrow[l,bend left=50,"R","\perp" swap]
\end{tikzcd}
\]

\end{document}