documentclass{article}
usepackage{tikz-cd}
begin{document}
begin{tikzcd}
UL
arrow{r}{{begin{tikzcd}1arrow{r}{a}&2end{tikzcd}}}
&UR
\
DL
arrow{r}
&DR
end{tikzcd}
end{document}

documentclass{article}
usepackage{tikz-cd}
begin{document}
begin{tikzcd}
UL
arrow{r}{
    begin{tikzpicture}
        node(1){1};
        node(2)[right of=1]{2};
        draw[->](1)--node{a} (2);
    end{tikzpicture}}
%arrow[r, "{begin{tikzpicture}
%   node(1){1};
%   node(2)[right of=1]{2};
%   draw[->](1)--node{a} (2);
%end{tikzpicture}}"]
&UR
\
DL
arrow{r}
&DR
end{tikzcd}
end{document}

documentclass{article}
usepackage{tikz-cd}
begin{document}
begin{tikzcd}[row sep=tiny]
tikzset{%
  >/.tip={Stealth[length=2pt, width=6pt, inset=2pt]}
}
1 arrow[r, "a"] & 2 \
UL arrow[r] & UR \
DL arrow[r] & DR
end{tikzcd}
end{document}