Symmetric triangle inTikZ-cd

Question

I would like to draw a commutative triangle with tikzcd where the entries have different sizes.

 \[
  \begin{tikzcd}[column sep=15pt]
  \mathcal{C} \ar{rr}  \ar{dr} & & S(\tau) \ar{dl} \\
   & \mathsf{Set} &
  \end{tikzcd}
 \]

This produces a slight asymmetry (the arrow on the right is more slanted, and the middle entry is not in the middle):

One solution is to use the following tikzcd-option:

 cells={nodes={align=center,text width=\widthof{$S(\tau)$}}}

The output looks as follows:

But now the arrow doesn't start at the left entry. How to make this happen?

Answer 1

Update

This feature is mentioned in the TikZ manual, namely III.20.3.2.

\begin{tikzcd}[column sep={1cm,between origins}]
    \mathcal{C}\ar{rr}\ar{dr} && S(\tau,..............)\ar{dl} \\
    & \mathsf{Set}
\end{tikzcd}

Old Answer

The column-separating symbol & accepts an optional argument. Just like \\[6pt] does, &[6] adds the current col sep by 6...pt by default.

\documentclass[tikz,border=9]{standalone}
\usepackage{tikz-cd}
\begin{document}
    \begin{tikzcd}[column sep=15pt]
        \mathcal{C}\ar{rr}\ar{dr} &[6]& S(\tau)\ar{dl} \\
        & \mathsf{Set}
    \end{tikzcd}
\end{document}

Answer 2

You can add [start anchor={[xshift=-5pt]}] to shift the starting point of your arrow.

MWE

\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
 \[
  \begin{tikzcd}[column sep=15pt,cells={nodes={align=center,text width=\widthof{$S(\tau)$}}}]
  \mathcal{C} \ar[start anchor={[xshift=-5pt]}]{rr}  \ar{dr} & & S(\tau) \ar{dl} \\
   & \mathsf{Set} &
  \end{tikzcd}
 \]
\end{document} 

Answer 3

For a real symmetry speaking of the arrows, you will have to increase the width and the hight of the upper left node.

% arara: pdflatex

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

\begin{document}
\[
\begin{tikzcd}[column sep=15pt]
      \phantom{S(\tau)}\mathllap{\mathcal{C}}\ar{rr}\ar{dr} & & S(\tau)\ar{dl} \\
    & \textsf{Set}
\end{tikzcd}
\]
\end{document}

As you can see, the diagonal arrows are starting and ending in the very same place (but mirrored).

Answer 4

I propose a solution with the psmatrix environment:

\documentclass[pdf]{article}
\usepackage{pst-node}

\begin{document}

\[ \psset{arrows=->, arrowinset=0.25, linewidth=0.6pt, nodesep=2pt, rowsep=0.9cm, colsep=0.7cm}
\begin{psmatrix}
  \ \mathcal C & & S(\tau) \\%
   & \mathsf {Set}
%%%
 \ncline[nodesepB=1.5pt]{1,1}{1,3} \ncline{1,1}{2,2}
 \ncline[nodesepA=1pt]{1,3}{2,2}
\end{psmatrix}
\]
\end{document}