Globular cells in Tikz

Question

I would like to draw a globular cell for higher dimensional categories and cannot find how to bend arrows between arrows between arrows...etc. I know how to bend arrows between nodes, but cannot find how to do it between arrows. Thanks for your help.

Sorry! Here is the type of diagram I have in mind.

I think I have an excellent answer from Gonzalo. I simply have to edit some of the arrows. Thanks!

Answer 1

I'd suggest you to use the tikz-cd package (built upon TikZ) which makes the creation of diagrams an easy job; using empty labels you can assign names that can then be used to draw the "inner" arrows; a little example with bent arrows inside bent arrows inside bent arrows:

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

\begin{document}

\begin{tikzcd}[column sep=1.5cm]
A
  \arrow[r, out=90,in=90,looseness=2.4,"f",""{name=p, below,}] 
  \arrow[r, bend left=40, ""{name=q, above,}]
  \arrow[r, bend left=40, ""{name=v, below,}]  
  \arrow[r, bend right=40,""{name=s, above,}] 
  \arrow[r, bend right=40,""{name=w, below,}] 
  \arrow[r, out=-90,in=-90,looseness=2.4,swap,"g",""{name=t, above,}] 
  \arrow[from=p, to=q]
  \arrow[from=v,to=s]
  \arrow[from=w,to=t]
& B
  \arrow[r,"h"]  
& C 
  \arrow[r, out=90,in=90,looseness=1.4,"j", ""{name=L, below,}]  
  \arrow[r, out=-90,in=-90,looseness=1.4,swap,"k",""{name=M, above}] 
  \arrow[from=L,to=M,bend right=60,""{name=N, right}]
  \arrow[from=L,to=M,bend left=60,""{name=P, left}]
  \arrow[from=N,to=P,bend left=40]
  \arrow[from=N,to=P,bend right=40]
& D
\end{tikzcd}

\end{document}

The result:

And to reproduce the diagram uploaded after the edit to the question:

\documentclass{article}
\usepackage{xargs}
\usepackage{tikz-cd}
\usetikzlibrary{arrows.meta}

\newlength{\myline}% line thickness
\setlength{\myline}{1pt}
\newcommandx*{\triplearrow}[4][1=0, 2=1]{% #1 = shorten left (optional), #2 = shorten right (optionsl),
% #3 = draw options (must contain arrow type), #4 = path
  \draw[line width=\myline,double distance=3\myline,#3] #4;
  \draw[line width=\myline,shorten <=#1\myline,shorten >=#2\myline,#3] #4;
}

\begin{document}

\begin{tikzcd}[
  column sep=1.5cm,
  execute at end picture={\triplearrow{arrows={-Implies}}{(N) -- (P)}},
  every node/.append style={draw,fill}
  ]
\bullet
  \arrow[r, out=90,in=90,looseness=1.4, ""{name=L, below,}]  
  \arrow[r, out=-90,in=-90,looseness=1.4,swap,""{name=M, above}] 
  \arrow[Rightarrow,from=L,to=M,bend right=60,""{name=N, right}]
  \arrow[Rightarrow,from=L,to=M,bend left=60,""{name=P, left}]
&
\bullet
\end{tikzcd}

\end{document}

The result:

For the triple implies arrow I used John Kormylo's code in his answer to Custom arrow shaft in tikz.