documentclass{article}
usepackage{amsmath}
usepackage{tikz-cd}
usetikzlibrary{arrows, matrix}
tikzcdset{every label/.append style = {font = tiny}}
begin{document}
[begin{tikzcd}
0rar & mathrm{Hom}_R(L, E) arrow{r}{mathrm{Hom}(beta, mathrm{id}_E)} & mathrm{Hom}_R(N, E) arrow{r}{mathrm{Hom}(alpha, mathrm{id}_E)} & mathrm{Hom}_R(M, E)
end{tikzcd}]
end{document}

documentclass{article}
usepackage{amsmath}
usepackage{tikz-cd}
usetikzlibrary{arrows, matrix}
tikzcdset{every label/.append style = {font = tiny}}
begin{document}
[begin{tikzcd}[column sep=1.5cm]
0rar & mathrm{Hom}_R(L, E) arrow{r}{mathrm{Hom}(beta, mathrm{id}_E)} & mathrm{Hom}_R(N, E) arrow{r}{mathrm{Hom}(alpha, mathrm{id}_E)} & mathrm{Hom}_R(M, E)
end{tikzcd}]
end{document}