rectangular and triangular commutative diagram with curves

Question

Here is the diagram I want to draw:

Could anyone help me in drawing it please?

the curved arrows and the diagonal arrows, I do not know how to do this.

Answer 1

Curved arrows can be made using bend left or bend right. Use ur in the \arrow command to have the arrow point up one row and right one column. Similarly, uurr will go up 2 rows and right two columns.

\documentclass{article}

\usepackage{tikz-cd}

\begin{document}

\begin{tikzcd}
 & & D_{c(f)}\\
R\arrow[r] & \pi_{\alpha}D_{\alpha}\arrow[r,yshift=2pt,"c"]\arrow[r,yshift=-2pt,"d"']\arrow[ur]\arrow[d] & \pi_fD_{c(f)}\arrow[d]\arrow[u,"\pi_f"']\\
C\arrow[r]\arrow[rr, bend right,"F"']\arrow[ur]\arrow[u,dashed,"\exists!"]\arrow[uurr,bend left,"F"] & D\arrow[r] & E
\end{tikzcd}

\end{document}