In `tikz-cd`, define arrow style to add label/node by arrowhead?

Question

I’m writing a paper with a lot of commutative diagrams, using tikz-cd, and am using different styles to distinguish various classes of maps in the diagrams. For instance, injective maps have a hooked tail, defined and used by

\tikzset{inj/.code={\pgfsetarrowsstart{right hook}}}
\begin{tikzcd} A \ar[r,inj] & B \end{tikzcd}

There’s one I’m having trouble defining. It should produce, roughly, a subscripted “lw” beside the arrowhead, i.e.\ something like

\begin{tikzcd} A \ar[r,"lw"' very near end] & B \end{tikzcd}.

How can I define a style lw so that I can write \begin{tikzcd} A \ar[r,lw] & B \end{tikzcd} to get the subscripted “lw” beside the arrowhead as described above?

An attribute that simply adds a label "lw"' very near end as on the example above would be fine. However, if it’s possible to do something like placing a node relative to the arrowhead, so that one has the versatile syntax of node positioning to fine-tune the placement of the “lw”, that would be even better.

MWE:

\documentclass{standalone}
\usepackage{tikz-cd} \usetikzlibrary{arrows}
\begin{document}

% example of defining/using arrow styles:
\tikzset{inj/.code={\pgfsetarrowsstart{right hook}}}
\begin{tikzcd} A \ar[r,inj] & B \end{tikzcd}

% what I want to define a style for:
\begin{tikzcd} A \ar[r,"lw"' very near end] & B \end{tikzcd}

\end{document}

Answer 1

Pretty straight forward:

\tikzset{lw/.style={"lw"' very near end}}

If you want the possibility to add more settings to the label, you can do this:

\tikzset{
  lw/.style={"lw"'{very near end,#1}},
  lw/.default={}
}

You can then use the style without arguments (\ar[r,lw]), or with an argument (\ar[r,lw={blue}]).

\documentclass[border=5mm]{standalone}
\usepackage{amsmath}

\usepackage{tikz-cd}
\usetikzlibrary{arrows}
\tikzset{
  lw/.style={"lw"'{very near end,#1}},
  lw/.default={}
}
\begin{document}
\begin{tikzcd}
  A \ar[r,lw] & B  \ar[r,lw={pos=1,yshift=-2pt,blue,draw}] & C
\end{tikzcd}
\end{document}