Arrow fat at one end, narrowing at the other end

Question

I can find fat arrows and thin arrows,

I can find fancy curly arrows that start thin and get fat,

All I want is a basic arrow that is thick at the origin, and thin at the other end, indicating that we are going "from" a "larger" space "to" a smaller space.

For use in something like a commutative diagram.

Does tikz have any such thing?

Answer 1

Well, it's not perfect but maybe this can get you started:

Basically I just made an arrow tip with Latex followed by Triangle, and then used it as a decoration on the arrow line (which is drawn in white).

\documentclass{article}

\usepackage{tikz-cd}
\usetikzlibrary{decorations.markings}

\tikzset{mytip/.tip={Latex[{color=black, fill=white, length=5mm, width=1.5mm, sep=-.9mm}]Triangle[color=black, fill=white]},
    myarrow/.style={white, decoration={transform={xshift=2.75mm}, markings, mark=at position .5 with {\arrow{mytip}}}, postaction=decorate}
    }

\begin{document}

\begin{tikzcd}[arrows={myarrow}]
K\arrow[dr]\\
\Omega\arrow[u]\arrow[r] & k
\end{tikzcd}

\end{document}

Answer 2

You second sketch is much easier to implement, I believe.

Idea:

1. Get the length of the path. (This only permits one segment, i.e. one line-to or one curve-to.)
2. Use that length to set the length of the second arrow tip.

Unfortunately, when the Triangle tip becomes too sharp the head gets beveled off but the arrow tip defintion doesn't account for that and adjust the drawing which is why I'm using line join=round here for both parts.
Though, PGF still uses the length calculations as if the sharp angle would be drawn mitered.

Since I'm not in the mood to do the math to adjust for the lost length, I'm just using a factor of 1.1 to stretch the second tip to about its needed length. This works well enough in this example for straight lines and not so good for curved path (with bending). But that's partly the reason why I'm using draw=none (via \tikz@mode@drawfalse) to force the (remaining) line not be drawn.

Code

\documentclass[tikz]{standalone}
\usetikzlibrary{decorations,bending}
\usepackage{tikz-cd}
\makeatletter
\tikzset{
  ararrow/.default={open}{open},
  ararrow/.code 2 args={%
    \tikz@addoption{%
       \pgfset{tips=true}% draw tips even if the path isn't.
       \pgfgetpath\currentpath
       \pgfprocessround{\currentpath}{\currentpath}%
       \pgf@decorate@parsesoftpath{\currentpath}{\currentpath}%
       \pgfsetarrowsend{%. % dot not really needed when no line is drawn
         Triangle[
           length=1.1*(\pgf@decorate@totalpathlength-4pt+.5*\the\pgflinewidth),
           line join=round,#1]
         Triangle[angle'=60,length=+4pt,line join=round,#2]}%
       \tikz@mode@drawfalse % disable drawing of path
    }
  },
  ararrow **/.style={ararrow={}{}},     ararrow oo/.style={ararrow={open}{open}},
  ararrow *o/.style={ararrow={}{open}}, ararrow o*/.style={ararrow={open}{}},
}
\makeatother
\begin{document}
\begin{tikzcd}[/tikz/arrows={[bend]}]
 K \drar[ararrow o*] \ar[dr, ararrow **, controls={+(1.5,0.5) and +(1,0.8)}] \\
 \Omega \rar[ararrow] \uar[ararrow o*] & k
\end{tikzcd}
\end{document}

Output

Answer 3

You can create your own custom decoration. With the following, you can use options to customize the appearance of the arrow as described in the picture below.

\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations}

\newlength{\tailarrowtiplength}
\setlength{\tailarrowtiplength}{1em}
\newlength{\tailarrowtipwidth}
\newlength{\tailarrowtailwidth}
\newlength{\tailarrowjointwidth}

\pgfdeclaredecoration{tail arrow decoration}{initial}{
    \state{initial}[width=\pgfdecoratedpathlength, next state=final] {
        \pgfpathlineto{\pgfpoint{0pt}{0.5\tailarrowtailwidth}}
        \pgfpathlineto{\pgfpointadd{\pgfpointdecoratedpathlast}{\pgfpoint{-1\tailarrowtiplength}{0.5\tailarrowjointwidth}}}
        \pgfpathlineto{\pgfpointadd{\pgfpointdecoratedpathlast}{\pgfpoint{-1\tailarrowtiplength}{0.5\tailarrowtipwidth}}}
        \pgfpathlineto{\pgfpointdecoratedpathlast}
        \pgfpathlineto{\pgfpointadd{\pgfpointdecoratedpathlast}{\pgfpoint{-1\tailarrowtiplength}{-0.5\tailarrowtipwidth}}}
        \pgfpathlineto{\pgfpointadd{\pgfpointdecoratedpathlast}{\pgfpoint{-1\tailarrowtiplength}{-0.5\tailarrowjointwidth}}}
        \pgfpathlineto{\pgfpoint{0pt}{-0.5\tailarrowtailwidth}}
        \pgfpathclose
    }
    \state{final} {
        \pgfpathmoveto{\pgfpointdecoratedpathlast}
    }
}

\tikzset{
    tail arrow tip length/.code={
        \setlength{\tailarrowtiplength}{#1}
    },
    tail arrow tip width/.code={
        \setlength{\tailarrowtipwidth}{#1}
    },
    tail arrow tail width/.code={
        \setlength{\tailarrowtailwidth}{#1}
    },
    tail arrow joint width/.code={
        \setlength{\tailarrowjointwidth}{#1}
    },
    tail arrow tip length/.default={ 2em },
    tail arrow tip width/.default={ 2em },
    tail arrow tail width/.default={ 1em },
    tail arrow joint width/.default={ .2em },
    tail arrow/.style={
        tail arrow tip length,
        tail arrow tip width,
        tail arrow tail width,
        tail arrow joint width,
        decorate,
        decoration={tail arrow decoration}
    }
}

\begin{document}
\begin{tikzpicture}

\draw[tail arrow, tail arrow tip width=4em, tail arrow tip length=1em, tail arrow joint width=0.5em] (0,-1) -- (5,-2); 

\draw[tail arrow] (0,0) -- (5,0); 

% description of options

\draw[|-|, red] ([shift={(-2em,-1.5em)}]5,0) -- ([shift={(0em,-1.5em)}]5,0) node[below, midway, font=\ttfamily\scriptsize, align=center] {tail arrow \\ tip length};

\draw[|-|, red] ([shift={(0.5em,-1em)}]5,0) -- ([shift={(0.5em,1em)}]5,0) node[right, midway, font=\ttfamily\scriptsize, align=left] {tail arrow \\ tip width};

\draw[|-|, red] ([shift={(-2.5em,-0.1em)}]5,0) -- ([shift={(-2.5em,0.1em)}]5,0) node[above left, pos=0, font=\ttfamily\scriptsize, align=right] {tail arrow \\ joint width};

\draw[|-|, red] ([shift={(-0.5em,-0.5em)}]0,0) -- ([shift={(-0.5em,0.5em)}]0,0) node[left, midway, font=\ttfamily\scriptsize, align=right] {tail arrow \\ tail width};

\end{tikzpicture}
\end{document}

Applied in a tikzcd context, you could then do:

\documentclass[border=10pt]{standalone}
\usepackage{tikz-cd}
\usetikzlibrary{decorations}

% [above definitions]

\begin{document}

\begin{tikzcd}[arrows={tail arrow, tail arrow tip width=.75em, tail arrow tail width=.5em, tail arrow tip length=1em}]
K\arrow[dr]\arrow[d]\\
\Omega\arrow[r] & k
\end{tikzcd}

\end{document}