Diagrams in category theory

You can easily draw your diagrams with the free online tool tikzcd-editor.

Screenshot:

Generated Code by clicking the {} button (not an MWE):

\begin{tikzcd}
A \arrow[d, "g"] \arrow[r, "f"] & B \arrow[r, "\alpha"] \arrow[d, "\gamma"] & D \arrow[d, "\beta"] \\
C \arrow[rru, "h"] & B' \arrow[r, "\lambda"] & D'
\end{tikzcd}

Link to live example

Here is a proposal.

\documentclass{article} 
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}  
A \arrow[r,"b"] \arrow[d,"g"] & C \arrow[r,"\alpha"] \arrow[d,"\gamma",pos=0.4,swap]& D \arrow[d,"\beta"]\\
B \arrow[rru,"h",pos=0.7,swap] & B' \arrow[r,"\omega"] & D'
\end{tikzcd}
\end{document}

I added the proposal to prove that users are willing to help. However, the purpose of this site is not to get screen shots converted to LaTeX code. Rather, the idea is that you try something, and if you get stuck, you have a code that you can show and others will help you solve that problem.

My code is only "basic".

\documentclass{standalone}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
A \arrow[r, "f"] \arrow[d, "g"'] & B \arrow[r, "\alpha"] \arrow[d, "h"'] & D \arrow[d, "\beta"] \\
C \arrow[rru, "\gamma"'] & B' \arrow[r, "\lambda"'] & D'
\end{tikzcd}
\end{document}