XY-pic LaTeX Diagrams Skill

XY-pic LaTeX Diagrams

Typeset commutative diagrams, automata, and categorical constructions using XY-pic in LaTeX, with inline Emacs preview via AUCTeX.

Setup

Preamble

\usepackage[all,cmtip]{xy}

all loads every XY-pic extension (matrix, arrow, curve, frame, etc.)
cmtip uses Computer Modern arrowheads (cleaner than default)

Emacs / AUCTeX preview

Add to init.el for inline C-c C-p C-p preview of xymatrix environments:

(eval-after-load "preview"
  '(add-to-list 'preview-default-preamble "\\PreviewEnvironment{xymatrix}" t))

Ensure PDF mode is active: C-c C-t C-p.

Core Syntax

Diagrams are matrices. & separates columns, \\ separates rows. Arrows use \ar[direction] where direction combines: u(up), d(down), l(left), r(right).

Commutative Square

\[
\xymatrix{
  A \ar[r]^f \ar[d]_g & B \ar[d]^h \\
  C \ar[r]_k           & D
}
\]

Arrow Labels

| Syntax | Position | |----------------|-----------------------------| | \ar[r]^f | label above/right of arrow | | \ar[r]_f | label below/left of arrow | | \ar[r]\|f | label on arrow (breaks it) | | \ar[r]|-{f} | label in gap on arrow |

Arrow Styles

\ar@{->}[r]        % normal (default)
\ar@{.>}[r]        % dotted
\ar@{=>}[r]        % double (natural transformation)
\ar@{-->}[r]       % dashed
\ar@{~>}[r]        % squiggly
\ar@{->>}[r]       % two-headed (epi)
\ar@{^{(}->}[r]    % hook (mono)
\ar@{=}[r]         % equals
\ar@{}[r]          % phantom (for label placement only)

Curved Arrows

\ar@/^/[r]^f       % curve up/right
\ar@/_/[r]_g       % curve down/left
\ar@/^1pc/[r]      % curve with specific radius
\ar@(ur,dr)[r]     % loop from upper-right to down-right

Spacing Control

\xymatrix@R=2pc@C=3pc{...}    % set row/column spacing
\xymatrix@C-1pc{...}           % reduce column spacing by 1pc
\xymatrix@1{...}               % entries are 1em wide

Common Diagram Patterns

Pullback / Fiber Product

\[
\xymatrix{
  U \ar@/_/[ddr]_y \ar@/^/[drr]^x \ar@{.>}[dr]|-{(x,y)} \\
  & X \times_Z Y \ar[d]^q \ar[r]_p & X \ar[d]_f \\
  & Y \ar[r]^g                      & Z
}
\]

Short Exact Sequence

\[
\xymatrix{
  0 \ar[r] & A \ar[r]^i & B \ar[r]^p & C \ar[r] & 0
}
\]

Adjunction

\[
\xymatrix@C=4pc{
  \mathcal{C} \ar@<1ex>[r]^{F} \ar@{}[r]|{\perp}
  & \mathcal{D} \ar@<1ex>[l]^{G}
}
\]

Natural Transformation (2-cell)

\[
\xymatrix{
  \mathcal{C} \rtwocell^F_G{\alpha} & \mathcal{D}
}
\]

(Requires \usepackage[all,2cell]{xy} \UseTwocells)

Long Exact Sequence (wrapping)

\[
\xymatrix{
  \cdots \ar[r] & H_n(A) \ar[r]^{i_*} & H_n(X) \ar[r]^{j_*}
  & H_n(X,A) \ar[dll]_{\partial} \\
  & H_{n-1}(A) \ar[r]^{i_*} & H_{n-1}(X) \ar[r] & \cdots
}
\]

Cube Diagram

\[
\xymatrix{
  A \ar[rr] \ar[dd] \ar[dr] && B \ar[dd] \ar[dr] \\
  & C \ar[rr] \ar[dd]       && D \ar[dd]          \\
  E \ar[rr] \ar[dr]         && F \ar[dr]           \\
  & G \ar[rr]                && H
}
\]

Automaton (DFA)

\[
\xymatrix{
  *+[o][F-]{q_0} \ar[r]^a \ar@(ul,dl)[]_b
  & *+[o][F=]{q_1} \ar@/^/[r]^a \ar@(ur,dr)[]^b
  & *+[o][F-]{q_2} \ar@/^/[l]^{a,b}
}
\]

*+[o][F-] = circle, single border
*+[o][F=] = circle, double border (accepting state)

Tips

Diagonal arrows: \ar[dr] goes down-right, \ar[ull] goes up-left-left (two columns)
Phantom arrows \ar@{}[r]|{\cong} place a symbol between entries without drawing
Compile twice if arrow positions look wrong on first pass
Debugging: add \entrymodifiers={+!!<0pt,\fontdimen22\textfont2>} to baseline-align entries
2-cells: load \usepackage[all,2cell]{xy} and \UseTwocells for natural transformations

Alternative: tikz-cd

For simpler syntax with TikZ backend:

\usepackage{tikz-cd}
\[
\begin{tikzcd}
  A \arrow[r, "f"] \arrow[d, "g"'] & B \arrow[d, "h"] \\
  C \arrow[r, "k"']                & D
\end{tikzcd}
\]

Both are available in texliveFull.

References

XY-pic User's Guide (PDF) — official reference
Alsani's examples (PDF) — beginner walkthrough
Milne's CD package comparison — xy-pic vs tikz-cd vs amscd
Debray's automata guide (PDF) — XY-pic for DFA/NFA
Run texdoc xypic locally for offline docs

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