[Tex/LaTex] Delayed drawing of arrows in tikz-cd

tikz-cdtikz-pgf

I want to draw an arrow which passes over another arrow in a tikz-cd commutative diagram. I can do that as follows from the documentation:

\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
\[
\begin{tikzcd}[ampersand replacement=\&,column sep=small]
  GM \arrow[pos=0.75]{rr}{\models_{M}}
     \arrow[two heads,swap]{dr}{e_{M}}
     \arrow[swap]{dd}{Gf}
     \&      \& 
     R^{FM}
       \arrow{dd}{R^{Ff}} \\
     \& T M 
    \arrow[tail,swap]{ru}{m_{M}}
    \arrow[swap,pos=0.75]{dd}{T f}
     \& \\
  GN \arrow[pos=0.75,crossing over]{rr}{\models_{N}}
     \arrow[two heads,swap]{dr}{e_{N}}
     \&      \& R^{FN} \\
     \& T N 
    \arrow[tail,swap]{ru}{m_{N}} \&    
\end{tikzcd}
\]
\end{document}

Result

However, I want the arrow $Tf$ pass over the arrow $\models_{N}$. (I.e. the over and under crossing reversed). But as the arrow, which is supposed to be drawn over the other, is drawn before the other the `crossing over' option does not work.

I tried to use nodes for the entries in the diagram to be able to draw the arrow later (from node to node), but that gives me a compile error. I can always return to plain tikz, but I guess others using tikz-cd might find it also helpful to know how to use nodes or delay drawing an arrow. Any hint?

Best Answer

Like this?

Result

Although I must confess I don't have yet the general solution, for this particular case the effect was achieved by drawing the arrow from TN to TM instead of TM to TN. This way the arrow was drawn after the horizontal one. And of course I used leftarrow to get the arrowtip right.

\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
\[
\begin{tikzcd}[ampersand replacement=\&,column sep=small]
  GM \arrow[pos=0.75]{rr}{\models_{M}}
     \arrow[two heads,swap]{dr}{e_{M}}
     \arrow[swap]{dd}{Gf}
     \&      \& 
     R^{FM}
       \arrow{dd}{R^{Ff}} \\
     \& T M 
    \arrow[tail,swap]{ru}{m_{M}}
     \& \\
  GN \arrow[pos=0.75,crossing over]{rr}{\models_{N}}
     \arrow[two heads,swap]{dr}{e_{N}}
     \&      \& R^{FN} \\
     \& T N 
    \arrow[leftarrow,pos=0.25,crossing over]{uu}{T f}  % <<----- HERE
    \arrow[tail,swap]{ru}{m_{N}} \&    
\end{tikzcd}
\]
\end{document}

Update: a more general solution

The above solution is ad-hoc and works only for this particular example. The general solution would allow to draw any additional arrow between two any nodes of the already typeset commutative diagram.

The idea is the following. Since internally tikzcd uses a matrix of nodes to typeset each node of the diagram, why wouldn't be possible to use those nodes as part of a path drawn after the diagram?

The idea is reasonable, but there are some issues here:

  1. What are the names of each node in the diagram? Would it be possible to use the syntax [(name)] normally allowed inside a tikz matrix of nodes? Answer: no it is not possible, that would break the code of the \arrow macro, which relies in the auto-generated names for the nodes.
  2. Then there are autogenerated names? Which are those names? Answer: They all begin with \tikzmatrixname and have the suffix -row-column. So for example, the first node of this diagram, (with label GM) would be \tikzmatrixname-1-1, the central node (TM) is \tikzmatrixname-2-2, and so on.

  3. So it would be possible to add \draw (\tikzmatrixname-1-1) to[bend left] (\tikzmatrixname-2-2); for example, after the matrix is done? i.e: this for example:

    \begin{tikzcd}[ampersand replacement=\&,column sep=small]
  GM \arrow[pos=0.75]{rr}{\models_{M}}
  [...]
  \arrow[tail,swap]{ru}{m_{N}} \&
% After all nodes are in the matris, draw some extra arrows
\draw[bend left] (\tikzmatrixname-1-1) to[bend left] (\tikzmatrixname-2-2);
\end{tikzcd}

    Answer: Sadly, the answer is no, this is not possible because of the way tikcd handles the diagram. Inside the tikzcd environment, surprisingly enought, no tikz commands can be issued. Indeed, all tikz commands are undefined, because the tikzcd environment is not a tikzpicture environment. This explains why you cannot use \node, \draw nor any other command.

    What tikzcd does is, each time you use the command \arrow or other equivalent, to compute the appropiate \path command, but instead of "executing" it, it is stored in a list with all the other paths resulting from other \arrow commands. At the end of the tikzcd environment, a tikzpicture is created, which contains the matrix of nodes, and inside that picture, finally the list of \path commands is executed, drawing all the arrows.

So, what can we do?

It would be great if tikzcd provided a kind of \drawAtTheEnd command, which allows for storing any tikz drawing command in the same way that the list of paths, and execute that stored commands at the end of the tikzcd environment. This way we could add other arrows, decorations, define node coordinates with overlay, remember picture to be accessed from other parts of the page, etc.

In the meanwhile, I coded a hack which allows to insert a new path into the internal list used by tikzcd. The macro is called \latearrow and it takes four arguments:

  1. The tikz options of the arrow (you can pass colours, to paths, pos, etc
  2. The name of the starting node, without the \tikzmatrixnode part. I.e: to refer to GM node you will call it 1-1, the node TM will be 2-2, and so on.
  3. The name of the ending node (also without the \tikzmatrixnode part)
  4. The text for the label in the arrow.

Using that macro, you can first draw your complete commutative diagram except for the arrow from TM to TN, and then add that arrow at the end with the syntax:

\latearrow{pos=0.75,crossing over}{2-2}{4-2}{T f}

As said, it is a quick&dirty hack, and does not use the same syntax than other arrows, does not allow for style options for the label, and I'm not sure if it would break anything, but apparently it works. Here is the code:

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

\makeatletter
\def\latearrow#1#2#3#4{%
  \toks@\expandafter{\tikzcd@savedpaths\path[/tikz/commutative diagrams/every arrow,#1]}%
  \global\edef\tikzcd@savedpaths{%
    \the\toks@%
    (\tikzmatrixname-#2)% \noexpand\tikzcd@sourceanchor)%
    to%
    node[/tikz/commutative diagrams/every label] {$#4$}
    (\tikzmatrixname-#3)% \noexpand\tikzcd@targetanchor)
;}}
\makeatother

\begin{document}
\[
\begin{tikzcd}[ampersand replacement=\&,column sep=small]
  GM \arrow[pos=0.75]{rr}{\models_{M}}
     \arrow[two heads,swap]{dr}{e_{M}}
     \arrow[swap]{dd}{Gf}
     \&      \& 
     R^{FM}
       \arrow{dd}{R^{Ff}} \\
     \& T M 
    \arrow[tail,swap]{ru}{m_{M}}
     \& \\
  GN \arrow[pos=0.75]{rr}{\models_{N}}
     \arrow[two heads,swap]{dr}{e_{N}}
     \&      \& R^{FN} \\
     \& T N 
    \arrow[tail,swap]{ru}{m_{N}} \&
\latearrow{pos=0.75,crossing over}{2-2}{4-2}{T f}
\latearrow{red, bend left}{1-1}{2-2}{x}
\end{tikzcd}
\]
\end{document}

Note that I added a blue option to this arrow, to demonstrate that it works. Just for fun, I added also a red curved "late arrow" from GM to TM. This is the result:

Result

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