The original figure, I think, it is done with xy package. In fact the classic tips are the same. The font used it is (mtpro2) where in this link you can find the version lite.
I have changed the font with newtxtext
(clone of Times New Roman) and newtxmath
. I think that it is very close with your image.
\documentclass[a4paper,12pt]{article}
\usepackage[all]{xy}
\usepackage{newtxtext,newtxmath}
\begin{document}
\xymatrix@R=2pc@C=3pc{
& P \ar[d]^{id} \ar@{-->}[dl]_{\mu} &\\
M \ar[r]^{\varphi} & P\ar[r] & 0
}
\end{document}

Addendum 1: ## To have the twoheadrightarrow you can use the code \ar@{>>}
(see the MWE):
\documentclass[a4paper,12pt]{article}
\usepackage[all]{xy}
\usepackage{newtxtext,newtxmath}
\begin{document}
\xymatrix@R=2pc@C=3pc{
& P \ar[d]^{id} \ar@{-->}[dl]_{\mu} &\\
M \ar@{>>}[r]^{\varphi} & P\ar@{>>}[r] & 0
}
\end{document}

If you want the tips of tikz-cd you can use the options [all, cmtip]
:
\documentclass[a4paper,12pt]{article}
\usepackage[all,cmtip]{xy}
\usepackage{newtxtext,newtxmath}
\begin{document}
\xymatrix@R=2pc@C=3pc{
& P \ar[d]^{id} \ar@{-->}[dl]_{\mu} &\\
M \ar@{>>}[r]^{\varphi} & P\ar@{>>}[r] & 0
}
\end{document}
