TikzCD arrow "to path" tracing a path over nodes with sharper corners (i.e. how to change looseness)

Question

I have the following code

\begin{center}
\begin{tikzcd}
L \arrow[dd, color = red, shift right = 1pt] \arrow[dd, color = red, start anchor = -5, to path={..controls +(1.5,0).. (\tikztotarget)}] \arrow[d, color = red!50!blue, start anchor = -10, to path={..controls +(1.0,0).. (\tikztotarget)}] \arrow[d, "a", color = red!50!blue]  \arrow[r, "l", hook]   & M  \arrow[ldd, "h", shift right = 1pt]\arrow[ld, "j \circ h"', dashed, outer sep = -2pt, pos = 0.35] \\
A \arrow[d, "i", hook]                                               &                                        \\
I \arrow[u, "j", bend left, color = blue]                                          &                                       
\end{tikzcd}
\end{center}

which produces the following picture:

I got the "to path" idea from https://tools.ietf.org/doc/texlive-doc/latex/tikz-cd/tikz-cd-doc.pdf (section "Tweaking to paths").

I am not quite happy with this picture because of the bend of the curved arrows; I would like them to be have a sharper corner at the node M, and be mostly parallel to the black arrows. Is this possible?

Answer 1

One possibility is to use tikzmark. You must compile twice.

\documentclass{article}
\usepackage{tikz-cd}
\usetikzlibrary{tikzmark}
\begin{document}
\begin{tikzcd} 
L\tikzmark{L}\arrow[dd, color = red, shift right = 1.2pt] \arrow[d, "a", color = red!50!blue]  \arrow[r, "l", hook, shift left=1pt]   & \tikzmark{M}M  \arrow[ldd, "h", shift right = 1pt]\arrow[ld, "j \circ h"', dashed, outer sep = -2pt, pos = 0.35] \
A\tikzmark{A}\arrow[d, "i", hook]\
I\tikzmark{I}\arrow[u, "j", bend left, color = blue]

\end{tikzcd}
%
\begin{tikzpicture}[remember picture, overlay]
\draw[red, ->, rounded corners]([shift={(1.6mm,.8mm)}]pic cs:L)to([shift={(.9mm,.8mm)}]pic cs:M)to([shift={(.3mm,4.2mm)}]pic cs:I);
\draw[red!50!blue, ->, rounded corners]([shift={(1.6mm,.4mm)}]pic cs:L)to([shift={(.6mm,.4mm)}]pic cs:M)to([shift={(1.3mm,3.5mm)}]pic cs:A);
\end{tikzpicture}
\end{document}