Argthtjtr

documentclass[12pt,reqno,a4paper]{amsart}

usepackage{extsizes}

usepackage{blindtext}

textheight 9.3in textwidth 6.5in

calclayout

usepackage{amsmath,amsthm,amsfonts,amssymb}

usepackage{hyperref}

usepackage{mathrsfs}

usepackage[all]{xy}

usepackage[normalem]{ulem}

usepackage{tikz-cd}

usepackage[utf8]{inputenc}

usepackage[english]{babel}

begin{document}

[begin{tikzcd}

underline{V} 

arrow[rrrrdd,  bend left]

arrow[rrdddd, bend right] arrow[rrdd, dotted] &  &&  & \

& & &  & \

&  & A arrow[dd] arrow[rr] &  & B arrow[dd] \

&  &  &  & \

&  & C arrow[rr] &  & D                

end{tikzcd}]

end{document}

above code is giving me following diagram

I used "phantom" technique to number part of commutative diagram. It did not work. I want to write

• (1) in the diagram enclosed by V,A,B


• (2) in the diagram enclosed by V,A,C


• (3) in the diagram enclosed by A,B,C,D

Can some one help me to see how to do this?

Is this what you mean?

You can add the labels to your diagram with no arrows:

[begin{tikzcd}

underline{V} 

arrow[rrrrdd,  bend left]

arrow[rrdddd, bend right] arrow[rrdd, dotted] &  &&  & \

& & (1) &  & \

& (2) & A arrow[dd] arrow[rr] &  & B arrow[dd] \

&  &  & (3) & \

&  & C arrow[rr] &  & D                

end{tikzcd}]

Just for fun: tikz-cd is based on TikZ so

documentclass[tikz]{standalone}

begin{document}

begin{tikzpicture}[y=0.8cm]

node (a) at (0,0) {$A$};

node (b) at (2,0) {$B$};

node (c) at (0,-2) {$C$};

node (d) at (2,-2) {$D$};

node (v) at (-2,2) {$underline{V}$};

draw[->] (a)--(b);

draw[->] (b)--(d);

draw[->] (a)--(c);

draw[->] (c)--(d);

draw[dotted,->] (v)--(a);

draw[->] (v) to[bend right] (c);

draw[->] (v) to[bend left] (b);

node at (1,-1) {(3)};

node at (0,1) {(1)};

node at (-1,0) {(2)};

end{tikzpicture}

end{document}

But I prefer this way (though the way I code it is not efficient)

documentclass[tikz]{standalone}

begin{document}

begin{tikzpicture}[y=0.8cm,>=stealth]

node (V) at (-2,2) {phantom{$underline{V}$}};

node (B) at (2,0) {phantom{$B$}};

node (C) at (0,-2) {phantom{$C$}};

fill[yellow!50] (0,0) rectangle (2,-2);

fill[green!20] (V) to[bend left] (B)--(2,0)--(0,0)--(V);

fill[blue!20] (V) to[bend right] (C)--(0,-2)--(0,0)--(V);

begin{scope}[every node/.style={fill=white,circle,draw}]

    node (a) at (0,0) {$A$};

    node (b) at (2,0) {$B$};

    node (c) at (0,-2) {$C$};

    node (d) at (2,-2) {$D$};

    node (v) at (-2,2) {$underline{V}$};

end{scope}

draw[->] (a)--(b);

draw[->] (b)--(d);

draw[->] (a)--(c);

draw[->] (c)--(d);

draw[dashed,->] (v)--(a);

draw[->] (v) to[bend right] (c);

draw[->] (v) to[bend left] (b);

node at (1,-1) {(3)};

node at (0,1) {(1)};

node at (-1,0) {(2)};

end{tikzpicture}

end{document}

With phantom arrows:

documentclass[a4paper]{article}

usepackage{tikz-cd}



begin{document}



[

begin{tikzcd}[nodes in empty cells]

underline{V}

  arrow[rrrrdd,  bend left]

  arrow[rrdddd, bend right]

  arrow[rrdd, dotted]

  arrow[rrrrdd,phantom,"(1)" description]

  arrow[rrdddd,phantom,"(2)" description]

\

&&&&\

&& A arrow[dd] arrow[rr] & arrow[dd,phantom,"(3)" description] &

B arrow[dd] \

&&&&\

&& C arrow[rr] && D

end{tikzcd}

]



end{document}