[Tex/LaTex] How to draw this commutative diagram for function composition

diagramstikz-pgfxy-pic

I am working on a project, and need to add a diagram that displays a commutative diagram illustrating basic function composition similar to what is on page 17 in the image attached. I would like to make it look a bit "nicer" for lack of a better term though. I really do not know where to even begin however. Any help is appreciated.

enter image description here

Here is a beginning. While I realize it is only a beginning, it is all I have been able to put together thus far. Thanks:

\documentclass[a4paper,12pt]{article}

\usepackage{tikz}
\usetikzlibrary{matrix,arrows}

\begin{document}
\begin{tikzpicture}[description/.style={fill=white,inner sep=2pt}]
\matrix (m) [matrix of math nodes, row sep=3em,
column sep=2.5em, text height=1.5ex, text depth=0.25ex]
{ X & & Y \\
& V & \\ };
%\draw[double,double distance=5pt] (m-1-1) – (m-1-3);
\path[-,font=\scriptsize]
(m-1-1) edge node[auto] {$ f $} (m-1-3)
edge node[description] {$ g \circ f $} (m-2-2)
(m-1-3) edge node[auto] {$ g $} (m-2-2);
\end{tikzpicture}

\end{document}

It does not have the arrows nor the ellipses I would like, but it is a start. Thanks again for the help!

Best Answer

You can add the option -> to draw the arrows. To add the ellipses, load the shapes.geometric library, and add

nodes={ellipse,draw,minimum width=<length>}

to the list of options for the \matrix command. Here, ellipse causes the node to have an elliptical shape, draw draws the elliptical border of the node, and minimum width=<length> specifies the minimal width of the node.

Code

\documentclass[border=2pt]{standalone}

\usepackage{tikz}
\usetikzlibrary{matrix,arrows,shapes.geometric}

\begin{document}

\begin{tikzpicture}[description/.style={fill=white,inner sep=2pt}]
  \matrix (m)[matrix of math nodes,
    row sep=3em,column sep=2.5em,
    text height=1.5ex, text depth=0.25ex,
    nodes={ellipse,draw,minimum width=2cm},
  ]{
    X && Y \\
    & V & \\
  };
  \path[->,font=\scriptsize]
  (m-1-1) edge node[auto] {$ f $} (m-1-3)
  edge node[description] {$ g \circ f $} (m-2-2)
  (m-1-3) edge node[auto] {$ g $} (m-2-2);
\end{tikzpicture}

\end{document}

Output

enter image description here

Upadate

An example that more closely resemble your picture:

Code

\documentclass[border=2pt]{standalone}

\usepackage{tikz}
\usetikzlibrary{calc,positioning,shapes.geometric}

\begin{document}

\begin{tikzpicture}
  \tikzset{
    elps/.style 2 args={draw,ellipse,minimum width=#1,minimum height=#2},
    node distance=3cm,
    font=\footnotesize,
    >=latex,
  }
  \node(x)[elps={1.3cm}{1cm},label={below left:$X$}]{};
  \node(y)[elps={2cm}{1.2cm},right=of x,label={below left:$Y$}]{};
  \node(v)[elps={1.5cm}{.9cm},below right=2cm of x,label={below left:$V$}]{};
  \fill[gray!50]($(y.center)-(5pt,5pt)$)circle[x radius=.7cm,y radius=.3cm]coordinate(im);
  \node at (im){$\mathrm{im}(f)$};
  \draw[->](x)to[bend right]node[above right]{$g\circ f$}(v);
  \draw[->](y)to[bend left]node[right]{$g$}(v);
  \draw[->](x)to[bend left=20]node[above]{$f$}(y);
\end{tikzpicture}

\end{document}

Output

enter image description here

Related Solutions

[Tex/LaTex] Can’t draw a commutative diagram

Here's one possible solution for the lower part using both xy and tikz-cd:

\documentclass{article}
\usepackage[all]{xy}
\usepackage{tikz-cd}

\begin{document}

$\xymatrix{
& S \ar[ld]^{\pi_{i}} \ar[rd]_{\pi_{j}} &\\
R_{i} \ar[rr]_{\mu_{ji}} & & R_{j} }$

\begin{tikzcd}[column sep=normal]
& S \arrow{dl}{\pi_{i}}\arrow{dr}[swap]{\pi_{j}} & \\
R_{i} \arrow{rr}[swap]{\mu_{ji}} & & R_{j}
\end{tikzcd}

\end{document}

enter image description here

Here's the complete diagram using tikz-cd:

\documentclass{article}
\usepackage{tikz-cd}

\begin{document}

\begin{tikzcd}[column sep=normal,row sep=large]
& Y\arrow{ddl}[swap]{\psi_{i}}\arrow{ddr}{\psi_{j}}\arrow{d}{h} & \\
& S \arrow{dl}{\pi_{i}}\arrow{dr}[swap]{\pi_{j}} & \\
R_{i} \arrow{rr}[swap]{\mu_{ji}} & & R_{j}
\end{tikzcd}

\end{document}

enter image description here

And now using xy:

\documentclass{article}
\usepackage[all]{xy}

\begin{document}

$\xymatrix{
& Y\ar[ldd]_{\psi_{i}}\ar[rdd]^{\psi_{j}}\ar[d]^{h} & \\
& S \ar[ld]^{\pi_{i}} \ar[rd]_{\pi_{j}} & \\
R_{i} \ar[rr]_{\mu_{ji}} & & R_{j} }$

\end{document}

enter image description here

And now, as requested in a comment, with some arrows curved:

\documentclass{article}
\usepackage{tikz-cd}

\begin{document}

\begin{tikzcd}[column sep=normal,row sep=large]
& Y\arrow[bend right]{ddl}[swap]{\psi_{i}}\arrow[bend left]{ddr}{\psi_{j}}\arrow{d}{h} & \\
& S \arrow{dl}{\pi_{i}}\arrow{dr}[swap]{\pi_{j}} & \\
R_{i} \arrow{rr}[swap]{\mu_{ji}} & & R_{j}
\end{tikzcd}

\end{document}

enter image description here

And with xy:

\documentclass{article}
\usepackage[all]{xy}

\begin{document}

$\xymatrix{
& Y\ar@/_/[ldd]_{\psi_{i}}\ar@/^/[rdd]^{\psi_{j}}\ar[d]^{h} & \\
& S \ar[ld]^{\pi_{i}} \ar[rd]_{\pi_{j}} & \\
R_{i} \ar[rr]_{\mu_{ji}} & & R_{j} }$

\end{document}

enter image description here

[Tex/LaTex] How to define the default vertical distance between nodes

I don't really get the question so I hope this is what you wanted. If you include a full document (such that we copy paste and see the problem on our systems) things are much more easier.

Here, you can change the default setting within a scope but your block style had a node distance which was resetting every time it is issued. I've made it 2mm such that we can see the difference easier.

\documentclass[tikz]{standalone}
\usetikzlibrary{arrows,shapes.geometric,positioning}

\begin{document}
\begin{tikzpicture}[decision/.style={diamond, draw, text width=4.5em, text badly centered, node distance=3.5cm, inner sep=0pt},
                    block/.style   ={rectangle, draw, text width=6em, text centered, rounded corners, minimum height=4em, minimum height=2em},
                    cloud/.style   ={draw, ellipse, minimum height=2em},
                    line/.style    ={draw,-latex'},
                    node distance = 1cm, 
                    auto]
    \node [block] (1st) {1st};
    \node [block, right= of 1st]  (2nd1) {2nd1};
\begin{scope}[node distance=2mm and 10mm]%Here we change it for everything inside this scope
    \node [block, above= of 2nd1] (2nd2) {2nd2};
    \node [block, below= of 2nd1] (2nd3) {2nd3};
    \node [block, right= of 2nd1] (3rd1) {3rd1};
    \node [block, above= of 3rd1] (3rd2) {3rd2};
    \node [block, above= of 3rd2] (3rd3) {3rd3};
\end{scope}
    \node [block, below= of 3rd1] (3rd4) {3rd4};
    \node [block, below= of 3rd4] (3rd5) {3rd5};

    \path [line] (1st) -- (2nd1);
    \path [line] (2nd1) -- (2nd2);
    \path [line] (2nd1) -- (2nd3);
    \path [line] (2nd2) -- (3rd3);
    \path [line] (2nd1) -- (3rd1);
    \path [line] (1st) -- (2nd1);
\end{tikzpicture}
\end{document}

enter image description here

Best Answer

Code

Output

Upadate

Code

Output

Related Solutions

[Tex/LaTex] Can’t draw a commutative diagram

[Tex/LaTex] How to define the default vertical distance between nodes

Related Question