Commutative diagram with 2 blocks

Question

Using the tikzcd package I would like to make the following diagram.

Answer 1

I suggest you to read the tikz-cd documentation and try it first, post some code of your try and then ask for help. However here it is.

\documentclass[margin=2mm]{standalone}
\usepackage{tikz-cd}
\begin{document}
    
\begin{tikzcd}[ execute at end picture={\draw[->] (-1,0) arc[start angle=-180,delta angle=300,radius=3mm];}]
A \arrow[d, "\alpha"] \arrow[r]     & B \arrow[r] \arrow[d, "\beta"]    & C \arrow[d, "\gamma"]\\
D \arrow[r]                         & E \arrow[r]                       & F
\end{tikzcd}
\end{document}

Answer 2

As an alternative to drawing and placing the circular arrow manually, you can use \circlearrowleft (scaled if you wish) on a phantom arrow from A to E.

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

\begin{document}
    
\begin{tikzcd}
A \arrow[d, "\alpha"]\arrow[r]\arrow[dr, phantom, "\scalebox{2}{$\circlearrowleft$}"] & B \arrow[r] \arrow[d, "\beta"] & C \arrow[d, "\gamma"]\\
D \arrow[r] & E \arrow[r] & F
\end{tikzcd}

\end{document}