How to draw tikz-cd diagram similar to the Snake Lemma diagram

Question

I would like to draw this diagram in tikz-cd. Specifically I would like the arrow to start 'from the top' of B here. I have looked at the example in the manual for tikz-cd, drawing the Snake Lemma, but it doesn't exactly explain anything well, and I have no idea what I'm doing regarding tikz in general. Is this easy at all to do?

To anyone asking why I would want to draw this diagram: I don't. I want to draw a diagram using similar arrows

Answer 1

A proof of concept example, see

• the user manual of tikz-cd v0.9f, sec. 3.1 "Tweaking to paths" and
• pgfmanual v3.1.8b, sec. 14.13 "The To Path Operation".

\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
  A & B \arrow[dl,
          to path={ |- ([shift={(3ex,2ex)}] \tikztostart.north) 
                    |- ([shift={(0, -2ex)}] \tikztotarget.south)
                    -- (\tikztotarget)
          }] \
  C & D
\end{tikzcd}
\end{document}

Answer 2

For fun, it is very simple with pstricks:

\documentclass{article}
\usepackage{pst-node}
\begin{document}
\[ \begin{psmatrix}[colsep=1.7cm]
        [name=A] A & [name=B] B \\
        [name=C] C & [name=D] D
    \end{psmatrix}
    \psset{linewidth=0.6pt, arrows=->, arrowinset=0.12, labelsep=1pt, nodesep=2pt}
    \ncline{A}{B}\naput{f} \ncline{A}{C}\nbput{g}
    \ncline{B}{D}\naput{h} \ncline{C}{D}\nbput{k}
    \ncloop[angleA=90, angleB=-90, loopsize=0.6, linearc=0.1]{B}{C}
     \]


\end{document}