Making a commutative diagram with circular arrows inside it, using tikzcd [duplicate]

Question

I am wondering how could I make the following commuting diagram

using only tikzcd. I have constructed the diagram without the circular arrows; you may find the code below. However, I don't know how to insert these arrows in the diagram. I am also interested in reproducing these kind of diagrams in the future, so I would really appreciate answers which could allow me to insert this type of node into other digrams.

Thanks in advance for your answers.

\documentclass[11pt,a4paper,twoside,leqno]{article}

\usepackage[utf8]{inputenc}
\usepackage[spanish]{babel}

\usepackage[left=2cm,right=2cm,top=2.5cm,bottom=2.5cm]{geometry}
\usepackage{blindtext}
\usepackage[nottoc,numbib]{tocbibind}
\usepackage{amsmath}
\usepackage{float}
\usepackage{booktabs}
\usepackage{amsfonts}
\usepackage{xcolor}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}
\usepackage{tikz-cd}
\usepackage[cal=euler,scr=boondox]{mathalpha}
\usepackage{cite}
\usepackage{graphicx}
\usepackage{fancyhdr}
\usepackage{tikz-cd}
\usepackage{centernot}
\usepackage{stmaryrd}
\usepackage{bm}
\usepackage[shortlabels]{enumitem}
\usepackage{scalerel}
\usepackage{tikz}
\usetikzlibrary{babel}
\usetikzlibrary{shadows,arrows,positioning,shapes.geometric}
\usetikzlibrary{decorations,decorations.markings}
\usetikzlibrary{3d}
\usepackage{pgfplots}
\usetikzlibrary{intersections, pgfplots.fillbetween}
\usetikzlibrary {arrows.meta}

\usepackage{etoolbox}
\usetikzlibrary{optics}
\usepackage{pgf,tikz}
\usetikzlibrary{arrows}
\begin{document}
    \begin{center}
    \begin{tikzcd}
        (\widetilde U,G,\varphi)&(\widetilde W,K,\xi)\arrow[l]\arrow[r]&(\widetilde V,H,\psi)\\
        (\widetilde U_x,G_x,\varphi_x)\arrow[u]&(\widetilde W_z,K_z,\xi_z)\arrow[l,dashed]\arrow[ul,dashed,name=U,"\lambda_{\widetilde U}"]\arrow[u]\arrow[ur,dashed,"\lambda_{\widetilde V}"']\arrow[r,dashed]&(\widetilde V_y,H_y,\psi_y)\arrow[u]
    \end{tikzcd}
\end{center}
\end{document}

Answer 1

It can be done with a phantom arrow, like this:

\documentclass[11pt,a4paper,twoside,leqno]{article}

\usepackage[utf8]{inputenc}
\usepackage[spanish]{babel}

\usepackage[left=2cm,right=2cm,top=2.5cm,bottom=2.5cm]{geometry}
\usepackage{blindtext}
\usepackage[nottoc,numbib]{tocbibind}
\usepackage{amsmath}
\usepackage{float}
\usepackage{booktabs}
\usepackage{amsfonts}
\usepackage{xcolor}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}
\usepackage{tikz-cd}
\usepackage[cal=euler,scr=boondox]{mathalpha}
\usepackage{cite}
\usepackage{graphicx}
\usepackage{fancyhdr}
\usepackage{tikz-cd}
\usepackage{centernot}
\usepackage{stmaryrd}
\usepackage{bm}
\usepackage[shortlabels]{enumitem}
\usepackage{scalerel}
\usepackage{tikz}
\usetikzlibrary{babel}
\usetikzlibrary{shadows,arrows,positioning,shapes.geometric}
\usetikzlibrary{decorations,decorations.markings}
\usetikzlibrary{3d}
\usepackage{pgfplots}
\usetikzlibrary{intersections, pgfplots.fillbetween}
\usetikzlibrary {arrows.meta}

\usepackage{etoolbox}
\usetikzlibrary{optics}
\usepackage{pgf,tikz}
\usetikzlibrary{arrows}

\begin{document}

    \begin{center}
    \begin{tikzcd}
        (\widetilde U,G,\varphi)&(\widetilde W,K,\xi)\arrow[l]\arrow[r]&(\widetilde V,H,\psi)\\
        (\widetilde U_x,G_x,\varphi_x)\arrow[u]\arrow[ur, phantom, "\scalebox{1.75}{$ \circlearrowleft $}", near end] &(\widetilde W_z,K_z,\xi_z)\arrow[l,dashed]\arrow[ul,dashed,name=U,"\lambda_{\widetilde U}"]\arrow[u]\arrow[ur,dashed,"\lambda_{\widetilde V}"']\arrow[r,dashed]&(\widetilde V_y,H_y,\psi_y)\arrow[u]\arrow[ul, phantom, "\scalebox{1.75}{$ \circlearrowright $}", near end]
    \end{tikzcd}
\end{center}

\end{document}