vertical $\cong$ or $\sym$ in xymatrix

Question

I need to show that a certain vertical arrow in a commutative diagram is an isomorphism. I would like to either add a $\sim$ next to the vertical line, rotated 90 degrees, or replace the arrow with a rotated $\cong$ symbol.

How can I implement either of these options with xymatrix?

To get a vertical ~, especially in XY, I usually use \wr. — Arun Debray, Nov 20 '15 at 19:57

MetalMathician · Answer 1 · 2017-01-18T13:59:04.797

You can also type \ar[d]^*[@]{\cong} this makes the symbol \cong follow the direction of the arrow, but it has some bugs, it won't work well if your arrow goes left. Or if you want to force a different direction try \ar[d]^*[@!180]{\cong} this rotates 180 degrees so, you'll get an upsidown \cong.

EDIT

So, I found in another post that I will cite in the comments, the solution for the arrows going left. This is a full example, with empty arrows using @{}.

\[\xymatrix{
\bullet&\bullet&\bullet\\
\bullet&\bullet\ar@{}[ru]|*[@]{\cong}
               \ar@{}[r]|*[@]{\cong}
               \ar@{}[rd]|*[@]{\cong}
               \ar@{}[d]|*[@]{\cong}
               \ar@{}[ld]|*[@]{\cong}
               \ar@{}[l]|*[@]{\cong}
               \ar@{}[lu]|*[@]{\cong}
               \ar@{}[u]|*[@]{\cong}&\bullet\\
\bullet&\bullet&\bullet
}\]

\[\xymatrix{
\bullet&\bullet&\bullet\\
\bullet&\bullet\ar@{}[ru]|*=0[@]{\cong}
               \ar@{}[r]|*=0[@]{\cong}
               \ar@{}[rd]|*=0[@]{\cong}
               \ar@{}[d]|*=0[@]{\cong}
               \ar@{}[ld]|*=0[@]{\cong}
               \ar@{}[l]|*=0[@]{\cong}
               \ar@{}[lu]|*=0[@]{\cong}
               \ar@{}[u]|*=0[@]{\cong}&\bullet\\
\bullet&\bullet&\bullet
}\]

The first xymatrix is the wrong one, and the second is the correct one. What the =0 does is to make the box of $\cong$ cero dimensional.

This is the other post http://tex.stackexchange.com/questions/38906/problems-rotating-arrow-labels and the solution appears to trace back to the answer of Ross Moore in http://tex.stackexchange.com/questions/6107/how-do-i-make-the-arrow-using-xymatrix — MetalMathician, Jan 18 '17 at 14:01

Sir Cornflakes · Answer 2 · 2017-01-14T22:11:19.733

5

You can always use \rotatebox{90}{$\cong$} (with \usepackage{graphicx})

edited Jan 14 '17 at 22:11

answered Nov 20 '15 at 17:25

Sir Cornflakes

3,582

thanks! it only worked in pdflatex, can't really explain why – Dima Sustretov Nov 20 '15 at 17:56
3

@DimaSustretov If you use a DVI viewer, be careful that rotation is not showed (but it will appear in print). – egreg Nov 20 '15 at 18:18
I like this, simple and effective! One can also use \rotatebox{-90}. – Lao-tzu May 20 '19 at 19:32

vertical $\cong$ or $\sym$ in xymatrix

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