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tikz-cd-doc.tex
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%% tikz-cd-doc.tex
%% Copyright 2011, 2012, 2014, 2018, 2021 Augusto Stoffel
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3
% of this license or (at your option) any later version.
% The latest version of this license is in
% http://www.latex-project.org/lppl.txt
% and version 1.3 or later is part of all distributions of LaTeX
% version 2005/12/01 or later.
%
% This work has the LPPL maintenance status `maintained'.
%
% The Current Maintainer of this work is Augusto Stoffel.
%
% This work consists of the files tikzlibrarycd.code.tex, tikz-cd.sty
% and tikz-cd-doc.tex.
%
% ------------------------------------------------------------------------
%
% This document requires the file pgfmanual-en-macros.tex (distributed
% with pgf) to compile. To get cross-references to the pgf manual,
% compile it and copy all resulting .aux files to the directory of
% tikz-cd-doc.tex.
\def\pgfautoxrefs{1}
\documentclass[a4paper]{ltxdoc}
\usepackage[hyphens]{url}
\def\xcolorversion{2.00}
\usepackage[version=latest]{pgf}
\usepackage{xkeyval,calc,listings,tikz,fp}
\usepackage{hyperref}
\hypersetup{%
colorlinks=false, % use true to enable colors below:
linkcolor=blue,%red,
filecolor=blue,%magenta,
pagecolor=blue,%red,
urlcolor=blue,%cyan,
citecolor=blue,
pdfborder=0 0 0,
}
% We need lots of libraries...
\usetikzlibrary{
arrows,
arrows.meta,
calc,
fit,
patterns,
plotmarks,
shapes.geometric,
shapes.misc,
shapes.symbols,
shapes.arrows,
shapes.callouts,
shapes.multipart,
shapes.gates.logic.US,
shapes.gates.logic.IEC,
circuits.logic.US,
circuits.logic.IEC,
circuits.logic.CDH,
circuits.ee.IEC,
datavisualization,
datavisualization.formats.functions,
er,
automata,
backgrounds,
chains,
topaths,
trees,
petri,
mindmap,
matrix,
calendar,
folding,
fadings,
shadings,
spy,
through,
turtle,
positioning,
scopes,
decorations.fractals,
decorations.shapes,
decorations.text,
decorations.pathmorphing,
decorations.pathreplacing,
decorations.footprints,
decorations.markings,
shadows,
lindenmayersystems,
intersections,
fixedpointarithmetic,
fpu,
svg.path,
external,
}
\usepackage[a4paper,left=2.25cm,right=2.25cm,top=2.5cm,bottom=2.5cm,nohead]{geometry}
\usepackage{amsmath,amssymb}
\usepackage{xxcolor}
\usepackage{pifont}
\usepackage{makeidx}
\usepackage{tikz-cd,xr,multicol,microtype}
\IfFileExists{pgfmanual-en-macros}
{\input{pgfmanual-en-macros}}
{\PackageError{tikz-cd-doc}{
This document requires the file pgfmanual-en-macros.tex (distributed
with pgf) to compile. Please place a copy of that file in the current
directory}{}}
\IfFileExists{pgfmanual.aux}
{\externaldocument[pgfman-]{pgfmanual}}
{\PackageWarning{tikz-cd-doc}{
Couldn't find pgfmanual.aux. To get cross-references to the pgf
manual, compile it and copy all resulting .aux files to the current
directory}{}}
\makeindex
% Global styles:
\tikzset{
every plot/.style={prefix=plots/pgf-},
shape example/.style={
color=black!30,
draw,
fill=yellow!30,
line width=.5cm,
inner xsep=2.5cm,
inner ysep=0.5cm}
}
\hypersetup{unicode,
pdftitle={tikzcd: Commutative diagrams with TikZ},
pdfkeywords={Commutative diagrams; TeX; LaTeX; ConTeXt; TikZ; pgf; tikz-cd; tikzcd},
}
\pgfkeys{
/pdflinks/search key prefixes in=
{/tikz/commutative diagrams/},%,/tikz/,/pgf/} % This really needs to be commented out!
/pdflinks/internal link prefix=tikzcd,
%
/pdflinks/warnings=false,
% for debugging:
/pdflinks/show labels=false,
}
\tikzset{/codeexample/every codeexample/.append style={/tikz/commutative diagrams/background color=graphicbackground}}
\tikzset{gray x/.tip={Rays[color=gray]}}
\newcommand{\displayarrow}[2][]{%
\index{#2@\protect\texttt{#2} arrow tip}%
\index{Arrow tips!#2@\protect\texttt{#2}}%
\texttt{#2} & yields \tikz[baseline=-axis_height] \draw[{#2}-{#2}, line width=rule_thickness, #1] (0,0) -- (1,0);}
\newcommand{\displayarrowstyle}[1]{
\def\mykey{/tikz/commutative diagrams/#1}%
\def\mypath{}%
\def\myname{}%
\firsttimetrue%
%\pgfmanualdecomposecount=0\relax%
\decompose/tikz/commutative diagrams/#1/\nil%
\texttt{#1} & yields
\tikz[baseline=-axis_height, line width=rule_thickness] \draw[arrows=gray
x-gray x,commutative diagrams/.cd, #1] (0,0) -- (0.6,0);}
\begin{document}
\begin{center}
\vspace*{1em}
\tikz\node[scale=1.2]{%
\color{gray}\Huge\ttfamily \char`\{\textcolor{red!75!black}{tikzcd}\char`\}};
\vspace{0.5em}
{\Large\bfseries Commutative diagrams with \tikzname}
\vspace{1em}
{Version 1.0 \qquad May 4, 2021}
\end{center}
\vspace{1.5em}
The general-purpose drawing package Ti\emph{k}Z can be used to typeset
commutative diagrams and other kinds of mathematical pictures,
generating high-quality results. The present package facilitates the
creation of such diagrams by providing a convenient set of macros and
reasonable default settings. Familiarity with Ti\emph{k}Z is helpful
but not necessary, since the examples contained here cover the most
common situations.
This work may be distributed and/or modified under the conditions of
the \LaTeX\ Project Public License, either version 1.3 of this license
or (at your option) any later version.
\tableofcontents
\section{Getting started}
\label{sec:basic-usage}
To load this package in \LaTeX, type
\begin{verse}
\index{tikz-cd@\protect\texttt{tikz-cd} package}%
\index{Packages and files!tikz-cd@\protect\texttt{tikz-cd}}%
|\usepackage{tikz-cd}|%
\end{verse}
or load \tikzname{} and then type
\begin{verse}%
\index{cd@\protect\texttt{cd} library}%
\index{Libraries!cd@\protect\texttt{cd}}%
|\usetikzlibrary{cd}|%
\end{verse}
This package is compatible with other \TeX\ formats as well.
See~\S\ref{sec:usage-plain-tex} and \S\ref{sec:usage-context}.
\subsection{Creating a diagram}
\label{sec:creating-diagrams}
The basic tool to create a commutative diagram is the following
environment.
\begin{environment}{{tikzcd}\opt{\oarg{options}}}
\end{environment}
The environment contents should describe a matrix, as in \LaTeX's
familiar |{tabular}| environment. The optional argument
\meta{options} may be used to modify the appearance of the diagram.
Any of the customization keys described in this manual, as well as
those originally provided by \tikzname{}, can be used here. Arrows
between matrix entries can be created with the |\arrow| command
described below.
Everything inside |{tikzcd}| is typeset in math mode, but you will
probably want to use it inside an |{equation}| environment or
|\[| \dots |\]|,
so that the diagram is placed on a new line and centered.
It is important to note that \textsc{dvi} viewers will not display
diagrams correctly. It is necessary to convert the \textsc{dvi} file
to \textsc{pdf} or \textsc{ps} format---or, even better, use a tool
that generates \textsc{pdf} files directly, such as \texttt{pdflatex}.
\subsection{Inserting arrows}
\label{sec:inserting-arrows}
Inside the |{tikzcd}| environment, the following synonymous commands
are provided to produce arrows.
\begin{pgfmanualentry}
\extractcommand\arrow|[|\meta{options}|]|\@@
\extractcommand\ar|[|\meta{options}|]|\@@
\pgfmanualbody
\end{pgfmanualentry}
Here, \meta{options} is a comma-separated list of options which can be
used to specify the arrow target, add labels, change arrow tips, and
perform additional modifications.
The arrow target can be specified by a direction parameter, which
consists of a string of characters |r|, |l|, |d|, |u| (standing for
right, left, down and up). Labels can be placed on an arrow by means
of the quotes syntax, described in detail in the \pgfname{} manual
\cite[\S\ref*{pgfman-section-label-quotes}]{pgfman}. Notice the use
of |"\phi"| in the example below.
\begin{codeexample}[]
\begin{tikzcd}
A \arrow[rd] \arrow[r, "\phi"] & B \\
& C
\end{tikzcd}
\end{codeexample}
To further modify the appearance of an arrow, note that \meta{options}
may contain any key that can be passed to \tikzname's |\path| command.
Similarly, a label can receive additional options via the syntax
\begin{verse}
|"|\meta{label text}|"|\opt{\meta{label options}}.
\end{verse}
Both \meta{label text} and \meta{label options} need to be enclosed in
curly braces if they contain commas.
{\catcode`\|=12
\begin{codeexample}[]
\begin{tikzcd}
A \arrow[r, "\phi"] \arrow[d, red]
& B \arrow[d, "\psi" red] \\
C \arrow[r, red, "\eta" blue]
& |[blue, rotate=-15]| D
\end{tikzcd}
\end{codeexample}
}
The example above also showcases one of the possible ways to pass
special options to a \tikzname\ matrix node. See the \pgfname{}
manual \cite[\S\ref*{pgfman-section-matrices}]{pgfman} for more
information.
Arrows can have an arbitrary number of labels, by repeated use of
arguments in quotes. The example below shows how to control the
positioning of labels. Notice in particular that an apostrophe as
\meta{label option} causes the label to be placed on the opposite side
of the arrow.
\begin{codeexample}[]
\begin{tikzcd}
A \arrow[r, "\phi" near start, "\psi"', "\eta" near end] & B
\end{tikzcd}
\end{codeexample}
We provide two real-life examples.
\begin{codeexample}[]
\begin{tikzcd}
T
\arrow[drr, bend left, "x"]
\arrow[ddr, bend right, "y"]
\arrow[dr, dotted, "{(x,y)}" description] & & \\
& X \times_Z Y \arrow[r, "p"] \arrow[d, "q"]
& X \arrow[d, "f"] \\
& Y \arrow[r, "g"]
& Z
\end{tikzcd}
\end{codeexample}
\begin{codeexample}[]
\begin{tikzcd}[column sep=tiny]
& \pi_1(U_1) \ar[dr] \ar[drr, "j_1", bend left=20]
&
&[1.5em] \\
\pi_1(U_1\cap U_2) \ar[ur, "i_1"] \ar[dr, "i_2"']
&
& \pi_1(U_1) \ast_{ \pi_1(U_1\cap U_2)} \pi_1(U_2) \ar[r, dashed, "\simeq"]
& \pi_1(X) \\
& \pi_1(U_2) \ar[ur]\ar[urr, "j_2"', bend right=20]
&
&
\end{tikzcd}
\end{codeexample}
\subsection{Changing arrow tips}
\label{sec:changing-arrow-tips}
A set of |\arrow| options is provided to create different kinds of
arrows. Some of these options have a short descriptive name, such as
|hook|, and others are named after \TeX{} arrow-producing commands
(without a ``|\|''), like |dashrightarrow|.%|
\begin{codeexample}[]
\begin{tikzcd}
X \arrow[r, hook] \arrow[dr, dashrightarrow]
& \bar{X} \arrow[d]\\
& Y
\end{tikzcd}
\end{codeexample}
The following list shows all available arrow types (each of them is a
style key located in |/tikz/commutative diagrams|).
\begin{multicols}{2}\raggedcolumns
\subsubsection*{Basic arrows}
\begin{tabular}{ll}
\displayarrowstyle{to head}\\
\displayarrowstyle{rightarrow}\\
\displayarrowstyle{leftarrow}\\
\displayarrowstyle{leftrightarrow}\\
\displayarrowstyle{Rightarrow}\\
\displayarrowstyle{Leftarrow}\\
\displayarrowstyle{Leftrightarrow}
\end{tabular}
\subsubsection*{Arrows from bar}
\begin{tabular}{ll}
\displayarrowstyle{maps to}\\
\displayarrowstyle{mapsto}\\
\displayarrowstyle{mapsfrom}\\
\displayarrowstyle{Mapsto}\\
\displayarrowstyle{Mapsfrom}\\
\end{tabular}
\subsubsection*{Arrows with hook}
\begin{tabular}{ll}
\displayarrowstyle{hook}\\
\displayarrowstyle{hook'}\\
\displayarrowstyle{hookrightarrow}\\
\displayarrowstyle{hookleftarrow}\\
\end{tabular}
\subsubsection*{Arrows with tail}
\begin{tabular}{ll}
\displayarrowstyle{tail}\\
\displayarrowstyle{rightarrowtail}\\
\displayarrowstyle{leftarrowtail}\\
\end{tabular}
\subsubsection*{Two-headed arrows}
\begin{tabular}{ll}
\displayarrowstyle{two heads}\\
\displayarrowstyle{twoheadrightarrow}\\
\displayarrowstyle{twoheadleftarrow}\\
\end{tabular}
\subsubsection*{Harpoons}
\begin{tabular}{ll}
\displayarrowstyle{harpoon}\\
\displayarrowstyle{harpoon'}\\
\displayarrowstyle{rightharpoonup}\\
\displayarrowstyle{rightharpoondown}\\
\displayarrowstyle{leftharpoonup}\\
\displayarrowstyle{leftharpoondown}\\
\end{tabular}
\subsubsection*{Dashed arrows}
\begin{tabular}{ll}
\displayarrowstyle{dashed}\\
\displayarrowstyle{dashrightarrow}\\
\displayarrowstyle{dashleftarrow}\\
\end{tabular}
\subsubsection*{Squiggly arrows}
\begin{tabular}{ll}
\displayarrowstyle{squiggly}\\
\displayarrowstyle{rightsquigarrow}\\
\displayarrowstyle{leftsquigarrow}\\
\displayarrowstyle{leftrightsquigarrow}
\end{tabular}
\subsubsection*{Non-arrows}
\begin{tabular}{ll}
\displayarrowstyle{no head}\\
\displayarrowstyle{no tail}\\
\displayarrowstyle{dash}\\
\displayarrowstyle{equal}\\
\end{tabular}
\end{multicols}
A gray cross (\tikz \path[/pgf/tips=true,gray x-] (0,0) -- (1mm,0);)
in the samples above indicates that the corresponding tip is kept
unchanged. This allows several arrow styles to be superimposed.
\begin{codeexample}[]
\begin{tikzcd}
A \arrow[r, tail, two heads, dashed] & B
\end{tikzcd}
\end{codeexample}
% It is also possible to select arrow tips using \tikzname{}'s |arrow|
% option directly (e.g., by saying |right hook->|). However, the method
% described here above is more appropriate, as it abstracts the choice
% of an actual arrow tip design (see also the |arrow style| key below),
% and is arguably better from the mnemonic standpoint.
\subsection{Alternative syntax for arrows}
\label{sec:altern-synt-arrows}
The following forms of the arrow command were used before the
appearance of the quotes syntax for labels, and now may seem somewhat
convoluted. They are nonetheless still available for backwards
compatibility.
\begin{command}{\arrow\opt{\oarg{options}}\marg{direction}\meta{labels}}
\end{command}
Here, \meta{direction} is a string containing the characters |r|, |l|,
|d|, |u| and is used to determine the arrow target. Alternatively,
you can specify an explicit matrix cell by replacing \meta{direction}
with something of the form \meta{row number}\texttt{-}\meta{column
number}, or the name of a node. The trailing \meta{labels} can be the
empty string or of the form
\begin{verse}
\opt{\oarg{label options}}\marg{label text}\meta{more labels}.
\end{verse}
The equivalent command |\ar| can also be used in this form. Here is
an example.
\begin{codeexample}[]
\begin{tikzcd}
A \arrow{d} \arrow{r}[near start]{\phi}[near end]{\psi}
& B \arrow[red]{d}{\xi} \\
C \arrow[red]{r}[blue]{\eta}
& D
\end{tikzcd}
\end{codeexample}
There are further shortened forms:
\begin{pgfmanualentry}
\extractcommand\rar\opt{\oarg{options}}\meta{labels}\@@
\extractcommand\lar\opt{\oarg{options}}\meta{labels}\@@
\extractcommand\dar\opt{\oarg{options}}\meta{labels}\@@
\extractcommand\uar\opt{\oarg{options}}\meta{labels}\@@
\extractcommand\drar\opt{\oarg{options}}\meta{labels}\@@
\extractcommand\urar\opt{\oarg{options}}\meta{labels}\@@
\extractcommand\dlar\opt{\oarg{options}}\meta{labels}\@@
\extractcommand\ular\opt{\oarg{options}}\meta{labels}\@@
\pgfmanualbody
\end{pgfmanualentry}
The first one is equivalent to
\begin{verse}
|\arrow|{\oarg{options}}|{r}|\meta{labels}
\end{verse}
and the other ones work analogously.
\subsection{Usage in plain \TeX{}}
\label{sec:usage-plain-tex}
To use this package in plain \TeX{}, load \tikzname{} and the
\texttt{cd} library by saying
\begin{verse}
|\input tikz.tex|\\
\index{cd@\protect\texttt{cd} library}%
\index{Libraries!cd@\protect\texttt{cd}}%
|\usetikzlibrary{cd}|
\end{verse}
The |{tikzcd}| environment should then be replaced by the following:
\begin{plainenvironment}{{tikzcd}\opt{\oarg{options}}}
\end{plainenvironment}
All other functions of this library work as described in this manual
without change.
\subsection{Usage in Con\TeX t}
\label{sec:usage-context}
To use this package in Con\TeX t, load \tikzname{} and then the
\texttt{cd} library by saying
\begin{verse}
|\usemodule[tikz]|\\
\index{cd@\protect\texttt{cd} library}%
\index{Libraries!cd@\protect\texttt{cd}}%
|\usetikzlibrary[cd]|
\end{verse}
The |{tikzcd}| environment should then be replaced by the following:
\begin{contextenvironment}{{tikzcd}\opt{\oarg{options}}}
\end{contextenvironment}
Moreover, you may replace the column and row separators |&|, |\\| by
their Con\TeX t analogues |\NC|, |\NR|. However, you should use |\NC|
only \emph{between} cells, and not before the first column or after
the last column, as in usual Con\TeX t tables. Similarly, |\NR|
should be used only between rows.
All other functions of this library work as described in this manual
without change.
\section{Controlling the appearance of diagrams}
\label{sec:chang-appe-diagr}
This section describes a number of customization keys defined by this
package. All keys are located in the path |/tikz/commutative diagrams|.
Options passed to |{tikzcd}| or |\arrow| are searched for
in that path, and, if not found there, in |/tikz|. To set options
globally, it is convenient to use the following command.
\begin{command}{\tikzcdset\marg{options}}
Executes \meta{options} in the path |/tikz/commutative diagrams|.
\end{command}
Besides the keys described in this manual, numerous \tikzname\
parameters can affect the appearance of a diagram. However, only a
few of them (namely those appearing in |every diagram|, |every cell|,
|every arrow|, and |every label| below) are reinitialized when
|{tikzcd}| is called. This means that modifying a certain \tikzname\
parameter globally may or may not affect the output of |{tikzcd}|.
We also point out that besides the options and styles provided by this
package, several keys defined by \tikzname{} are useful for arrows.
Some examples are \texttt{dashed}, |dotted|, and its relatives,
|line width=|\meta{dimension}, |color=|\meta{color}, |bend right|, |bend left|,
|in=|\meta{angle}, |out=|\meta{angle}, |loop|, etc. See the
\pgfname{} manual~\cite[\S\ref*{pgfman-section-cap-joins} and
\S\ref*{pgfman-library-to-paths}]{pgfman}. Likewise, \tikzname{}
provides several keys that are useful for labels, such as |above|,
|below|, |left|, |right|, |swap| (which makes the label be placed on
the right side of the arrow, relative to its direction), |sloped|,
|pos=|\meta{fraction}, |near start|, |near end|, |inner sep=|\meta{dimension},
|font=|\meta{font command}, |text width=|\meta{dimension}, etc. See the \pgfname{}
manual~\cite[\S\ref*{pgfman-section-nodes}, esp.\
\S\ref*{pgfman-section-pos-option}]{pgfman}.
\subsection{General options}
\label{sec:general-options}
\begin{stylekey}{/tikz/commutative diagrams/every diagram}
This style is applied to every |{tikzcd}| environment. Initially, it
contains the following:
\begin{verse}
|row sep=normal||,|\\
|column sep=normal||,|\\
|/tikz/baseline=0pt|
\end{verse}
\end{stylekey}
The |baseline=0pt| setting is used to make equation numbers be placed
correctly (as an exception, one-row diagrams are anchored at their
matrix base, which is exactly what you want).
\begin{key}{/tikz/commutative diagrams/diagrams=\meta{options}}
This key appends \meta{options} to the style |every diagram|.
\end{key}
\begin{stylekey}{/tikz/commutative diagrams/every matrix}
This style is applied to the \tikzname{} matrix created internally
by |{tikzcd}|. Initially, it contains the following:
\begin{verse}
|/tikz/inner sep=0pt|
\end{verse}
\end{stylekey}
\begin{stylekey}{/tikz/commutative diagrams/every cell}
This style is applied to every \tikzname{} matrix cell created by
|{tikzcd}|. Initially, it contains the following:
\begin{verse}
|/tikz/shape=asymmetrical rectangle||,|\\
|/tikz/inner xsep=1ex||,|\\
|/tikz/inner ysep=0.85ex|
\end{verse}
\end{stylekey}
The |asymmetrical rectangle| shape is described in
\S\ref{sec:asymm-rect-shape}. The |inner xsep|, |inner ysep| options
determine the spacing between a diagram entry and any arrows reaching
it.
\begin{key}{/tikz/commutative diagrams/cells=\meta{options}}
This key appends \meta{options} to the style |every cell|.
\end{key}
\def\printsepaux+#1em{#1\,em}
\def\printsep#1#2{\edef\temp{\pgfkeysvalueof{/tikz/commutative diagrams/#1 sep/#2}}\expandafter\printsepaux\temp}
\begin{key}{/tikz/commutative diagrams/row sep=\meta{size}}
This key acts as a frontend to \tikzname's |/tikz/row sep| key. If
the key
\begin{verse}
|/tikz/commutative diagrams/row sep/|\meta{size}
\end{verse}
stores a \meta{value}, then it is read and
|/tikz/row sep|=\meta{value} is set. If the key above is not
initialized, then \meta{size} is presumed to be a dimension, and
|/tikz/row sep|=\meta{size} is set.
The initially available sizes, and their values, are
the following:
\begin{center}
\begin{tabular}{cccccc}
|tiny| & |small| & |scriptsize| & |normal| & |large| & |huge| \\
\printsep{row}{tiny} & \printsep{row}{small} & \printsep{row}{scriptsize} & \printsep{row}{normal} & \printsep{row}{large} & \printsep{row}{huge}
\end{tabular}
\end{center}
\end{key}
Notice that setting, say, |row sep=1cm| globally with |\tikzcdset| will
have no effect, since the |row sep| option is re-set at the beginning
of each diagram. To make all diagrams have |row sep| equal to 1\,cm,
you can modify the meaning of |normal| by saying
\begin{verse}
|\tikzcdset{row sep/normal=1cm}|.
\end{verse}
You can also create new sizes, but note that \pgfname\ requires new keys to be
initialized explicitly. For example, to create a size |my size|,
meaning 1\,ex, you should use
\begin{verse}
|\tikzcdset{row sep/my size/.initial=1ex}|.
\end{verse}
\begin{key}{/tikz/commutative diagrams/column sep=\meta{size}}
This works analogously to the |row sep| key above. The sizes available
initially are the following:
\begin{center}
\begin{tabular}{cccccc}
|tiny| & |small| & |scriptsize| & |normal| & |large| & |huge| \\
\printsep{column}{tiny} & \printsep{column}{small} & \printsep{column}{scriptsize} & \printsep{column}{normal} & \printsep{column}{large} & \printsep{column}{huge}
\end{tabular}
\end{center}
\end{key}
\begin{key}{/tikz/commutative diagrams/sep=\meta{size}}
This key sets |row sep=|\meta{size}, |column sep=|\meta{size}.
\end{key}
In the examples below, the triangular diagrams would look too wide or
too tall if the column or row separation were not set appropriately.
\begin{codeexample}[]
\begin{tikzcd}[column sep=small]
& A \arrow[dl] \arrow[dr] & \\
B \arrow{rr} & & C
\end{tikzcd}
\end{codeexample}
\begin{codeexample}[]
\begin{tikzcd}[row sep=tiny]
& B \arrow[dd] \\
A \arrow[ur] \arrow[dr] & \\
& C
\end{tikzcd}
\end{codeexample}
Section \ref*{pgfman-section-matrices}.3.2 of the \pgfname{} manual
\cite{pgfman} contains further details on the spacing of matrix cells.
\begin{stylekey}{/tikz/commutative diagrams/cramped}
By default, a generous amount of white space is added around diagram
cells, which is appropriate for large, displayed diagrams. The
present style removes some of this extra white space, and is
intended for smaller diagrams that should blend with the surrounding
text, or very wide material that wouldn't fit the page otherwise.
\end{stylekey}
The picture below shows the (somewhat subtle) difference
between the cramped and the non-cramped styles.
\begin{codeexample}[pre=\minipage{6cm},post=\endminipage]
This \begin{tikzcd} A \arrow[r] & B \end{tikzcd} is a regular diagram.\\
This \begin{tikzcd}[cramped, sep=small] A \arrow[r] & B \end{tikzcd} is a cramped diagram.\\
This $A \to B$ is just a formula.
\end{codeexample}
Keep in mind that while there are some legitimate uses for |{tikzcd}|
diagrams on inline formulas, standard \LaTeX\ constructs such as
|\overset| and |\xrigthtarrow| are often sufficient and should be
preferred.
\begin{key}{/tikz/commutative diagrams/math mode=\meta{boolean}
(default true)}
This key determines whether or not the contents of a diagram are
typeset in math mode. If set globally or diagram-wise, it affects
both the diagram entries and arrow labels. If used with |\arrow|,
it affects only its labels.
\end{key}
\begin{key}{/tikz/commutative diagrams/background color=\meta{color} (initially white)}
This key stores the name of a color, and is read by
styles that fill the background, such as |description| and |crossing over|.
It does not cause the background of diagrams to be filled.
\end{key}
\subsection{Global options for arrows}
\label{sec:options-arrows}
\begin{stylekey}{/tikz/commutative diagrams/every arrow}
This style is applied to every |\arrow|. Initially, it contains the
following:
\begin{verse}
|/tikz/draw,|\\
|/tikz/line width=rule_thickness||,|\\
|rightarrow|
\end{verse}
\end{stylekey}
\begin{key}{/tikz/commutative diagrams/arrows=\meta{options}}
This key appends \meta{options} to the style |every arrow|.
\end{key}
\begin{key}{/tikz/commutative diagrams/arrow style=\meta{style}}
This key determines which collection of arrow tips is used by the
arrow tip selection styles listed in
\S\ref{sec:changing-arrow-tips}. The initial setting is suitable
for documents using the Computer Modern font at any size. The
available choices for \meta{style} are:
\begin{description}
\item[\texttt{Latin Modern}] A small variant of the initial
settings, intended for documents using the Latin Modern font at
any size.
\item[\texttt{math font}] This setting uses the |Glyph| meta arrow
tip described in \S\ref{sec:font-arrow-tips}.
\item[\texttt{tikz}] This setting uses the arrow tips defined in
\tikzname's |arrows.meta| library. It honors the option
|/tikz/>|.
\end{description}
This key is usually invoked in the document preamble, and should be
set only once.
\end{key}
If you are using a font different from Computer Modern or Latin
Modern, you may find the best results by selecting the |math font|
style. As detailed in \S\ref{sec:font-arrow-tips}, this is not
guaranteed to work perfectly with all fonts, but gives good results in
many cases. If the \texttt{math font} style gives unsatisfactory
results, you can try selecting the \texttt{tikz} style, and setting
|/tikz/>| to the value that best matches your font (among those shown
in \cite[\S\ref*{pgfman-section-arrows-meta}]{pgfman}).
\begin{codeexample}[]
% in preamble
\tikzcdset{
arrow style=tikz,
diagrams={>={Straight Barb[scale=0.8]}}
}
% in document body
\begin{tikzcd}
A \arrow[r, tail] \arrow[rd] & B \arrow[d, two heads]\\
& D
\end{tikzcd}
\end{codeexample}
\subsection{Absolute placement of arrows}
\label{sec:absol-positioning}
The usual behavior of |\arrow| is to produce an arrow starting at the
diagram entry where the command appears, and ending at an entry whose
location is specified relative to that. The following keys override
this behavior, allowing source and target to be selected explicitly.
\begin{key}{/tikz/commutative diagrams/from=\meta{argument}}
If \meta{argument} is of the form \meta{row
number}\texttt{-}\meta{column number}, or if it is a string of
characters |r|, |l|, |d|, |u|, this key sets the arrow source to be
the corresponding cell in the diagram matrix. Otherwise, it assumes
the argument is the name of a node and sets the arrow source to
\meta{argument}.
\end{key}
\begin{key}{/tikz/commutative diagrams/to=\meta{argument}}
Similar to |from|, but refers to the arrow target.
\end{key}
Recall that it is possible to give a specific entry of a \tikzname{}
matrix a name by using the \verb!|[!\meta{options}\verb!]|! syntax, as
done for entry $C$ in the example below. You must be careful not to
create nodes whose name contains only the characters |l|, |r|, |u|,
|d| if you want to refer to them using |from| or |to|. The following
illustrates several different uses of these keys.
{\catcode`\|=12
\begin{codeexample}[]
\begin{tikzcd}
A \arrow[to=Z, red] \arrow[to=2-2, blue]
& B \\
|[alias=Z]| C
& D
\arrow[from=ul, to=1-2, purple]
\end{tikzcd}
\end{codeexample}
}
In the next examples, empty labels are used to create nodes for later
reference. The |draw=red| option is used to show where these empty
nodes are located, but of course you want to remove that when using
this technique.
\begin{codeexample}[]
\begin{tikzcd}[column sep=scriptsize]
A \arrow[dr] \arrow[rr, ""{name=U, below, draw=red}]{}
& & B \arrow[dl] \\
& C \arrow[Rightarrow, from=U, "\psi"]
\end{tikzcd}
\end{codeexample}
\begin{codeexample}[]
\begin{tikzcd}
A \arrow[r, bend left=50, ""{name=U, below, draw=red}]
\arrow[r, bend right=50, ""{name=D, draw=red}]
& B
\arrow[Rightarrow, from=U, to=D]
\end{tikzcd}
\end{codeexample}
\subsection{Phantom arrows}
\label{sec:phantom-arrows}
Sometimes it is necessary to insert a symbol outside the grid
subjacent to the diagram. The easiest way to achieve this is as a
label to an invisible arrow.
\begin{stylekey}{/tikz/commutative diagrams/phantom}
Creates an invisible arrow. Labels to this arrow are not invisible.
They will be anchored at their center and typeset in full size
(i.e., with |\textstyle|). To get smaller labels, as in ordinary
arrows, use the |\scriptstyle| command.
\end{stylekey}
In the picture below, the arrow containing the |phantom| option goes from
$A$ to $D$, and the |\ulcorner| symbol ($\ulcorner$) is inserted
closer to the starting point $A$.
\begin{codeexample}[]
\begin{tikzcd}
A \arrow[r] \arrow[d] \arrow[dr, phantom, "\ulcorner", very near start]
& B \arrow[d] \\
C \arrow[r]
& D
\end{tikzcd}
\end{codeexample}
\subsection{Fine-tuning the placement of arrows}
\label{sec:fine-tuning-arrows}
\begin{key}{/tikz/commutative diagrams/shift left=\meta{dimension}
(default 0.56ex)}
Shifts arrows by \meta{dimension} to the left, relative to the arrow
direction. A dimensionless argument causes that multiple of the
default value to be used.
\end{key}
\begin{key}{/tikz/commutative diagrams/shift right=\meta{dimension}
(default 1)}
A shortcut to |shift left=-|\meta{dimension}.
\end{key}
\begin{codeexample}[]
\begin{tikzcd}
A \arrow[r, red, shift left=1.5ex] \arrow[r]
\arrow[dr, blue, shift right=1.5ex] \arrow[dr]
& B \arrow[d, purple, shift left=1.5ex] \arrow[d]\\
& C
\end{tikzcd}
\end{codeexample}
The default values of |shift left| and |shift right| are appropriate
for a pair of parallel arrows, and dimensionless arguments are useful
to create sets of multiple parallel arrows.
\begin{codeexample}[]
\begin{tikzcd}
A \arrow[r]
& B \arrow[r, shift left]
\arrow[r, shift right]
& C \arrow[r]
\arrow[r, shift left=2]
\arrow[r, shift right=2]
& \cdots
\end{tikzcd}
\end{codeexample}
\begin{key}{/tikz/commutative diagrams/shift=\marg{coordinate}}
Shifts arrows by \meta{coordinate}.
\end{key}
\begin{key}{/tikz/commutative diagrams/xshift=\meta{dimension}}
Shifts arrows right by \meta{dimension}.
\end{key}
\begin{key}{/tikz/commutative diagrams/yshift=\meta{dimension}}
Shifts arrows up by \meta{dimension}.
\end{key}
\begin{codeexample}[]
\begin{tikzcd}
A \arrow[r, yshift=0.7ex] \arrow[r, yshift=-0.7ex]
& B \arrow[d, xshift=0.7ex] \arrow[d, xshift=-0.7ex] \\
& C
\end{tikzcd}
\end{codeexample}
\begin{key}{/tikz/commutative diagrams/start anchor=\opt{{\ttfamily\char`\{}\ooarg{coordinate transformations}}\meta{anchor}\opt{\ttfamily\char`\}}}
This key specifies at which anchor of the source node the arrow
should start. Optionally, additional coordinate transformations can
be supplied. An empty \meta{anchor} argument causes no anchor to be
specified, which is the usual behavior.
\end{key}
\begin{key}{/tikz/commutative diagrams/end anchor=\opt{{\ttfamily\char`\{}\ooarg{coordinate transformations}}\meta{anchor}\opt{\ttfamily\char`\}}}
This key works analogously, but refers to the target node of the arrow.
\end{key}
See the picture on \S\ref{sec:asymm-rect-shape} for some of the
possible values for \meta{anchor}.
\begin{codeexample}[]
\begin{tikzcd}[cells={nodes={draw=gray}}]
A \arrow[r, black]
\arrow[r, blue, end anchor=north east]
\arrow[r,
red,
start anchor={[xshift=-1ex]},
end anchor={[yshift=2ex]north east}]
& B
\end{tikzcd}
\end{codeexample}
\begin{key}{/tikz/commutative diagrams/shorten=\meta{dimension}}
This key shortens each end of the arrow by \meta{dimension}.
\begin{codeexample}[]
\begin{tikzcd}
A \arrow[r, shift left]
\ar[r, shorten=2mm, shift right]
& B
\end{tikzcd}
\end{codeexample}
\end{key}
Note that the ends of an arrow can be shortened individually using
\tikzname's built-in keys |shorten <| and |shorten >|.
\subsection{Three-dimensional diagrams}
\label{sec:crossing-over}
\begin{stylekey}{/tikz/commutative diagrams/crossing over}
This style makes a thicker line, with color |background color|, to
be drawn under the current arrow, simulating the effect of its
passing over other arrows.
\begin{codeexample}[]
\begin{tikzcd}
A \arrow[dr] & B \arrow[dl, crossing over] \\
C & D