Hexagon commutative diagram in mathematics (Herbrand quotient diagram)

Question

The following code

\[
\begin{tikzpicture}[>=latex]
    \def\radius{3cm} % change to an appropriate value
    \node (h0A) at (60:\radius)   {$H^0(G,A)$};
    \node (h0C) at (0:\radius)    {$H^0(G,C)$};
    \node (h1B) at (-60:\radius)  {$H^1(G,B)$};
    \node (h1A) at (-120:\radius) {$H^1(G,A)$};
    \node (h1C) at (180:\radius)  {$H^1(G,C)$};
    \node (h0B) at (120:\radius)  {$H^0(G,B)$};
\path[-&gt;,font=\small]
    (h0A) edge node[auto] {$g_0$} (h0C)
    (h0C) edge node[auto] {$\delta_0$} (h1B)
    (h1B) edge node[auto] {$f_1$} (h1A)
    (h1A) edge node[auto] {$g_1$} (h1C)
    (h1C) edge node[auto] {$\delta_1$} (h0B)
    (h0B) edge node[auto] {$f_0$} (h0A);

\end{tikzpicture}]

But I want to exchange $A$ and $B$ and write the following diagram.
But when I exchange $A$ and $B$ in the above diagram, diagram is destroyed.
How can I write the diagram below in LaTeX?

Provided that you load the amssym package (you should always post complete MWEs including \documentclass and all relevant packages), you can put \node[rotate=180] at (0,0) {$\circlearrowright$}; to your document in order to typset the clockwise arrow in the center of your diagram. — Jasper Habicht, Dec 10 '23 at 08:37
@JasperHabicht - Great suggestion for the additional node; in fact, I've updated my answer to include [borrow?, steal??] your suggestion. (You're familiar with Picasso's saying in this regard, right?) — Mico, Dec 10 '23 at 09:02
@Mico Oh, sure! It should be considered implemeting an inspiration, I guess. I'd say that coding is almost always largely based on copying ... =) — Jasper Habicht, Dec 10 '23 at 09:12

Mico · Answer 1 · 2023-12-10T09:12:37.783

(too long for a comment, hence posted as an answer; updated to include @JasperHabicht's suggestion)

I do not find that the "diagram is destroyed" when I replace the letter sequence A-C-B-A-C-B in the node list with B-C-A-B-C-A.

Note that it's not necessary to update the six node names in a similar fashion. In fact, it might be good idea to label the nodes without reference to their contents. E.g., one might choose u, v, w, x, y, and z as the six node names.

\documentclass{article}
\usepackage{tikz,amssymb}
\begin{document}
[
\begin{tikzpicture}[>=latex]
    \def\radius{3.3cm} % choose an appropriate value
    \node (u) at ( 60:\radius) {$H^0(G,B)$};
    \node (v) at (  0:\radius) {$H^0(G,C)$};
    \node (w) at (300:\radius) {$H^1(G,A)$};
    \node (x) at (240:\radius) {$H^1(G,B)$};
    \node (y) at (180:\radius) {$H^1(G,C)$};
    \node (z) at (120:\radius) {$H^0(G,A)$};
\path[-&gt;]
      (u) edge node[auto] {$g_0$}      (v)
      (v) edge node[auto] {$\delta_0$} (w)
      (w) edge node[auto] {$f_1$}      (x)
      (x) edge node[auto] {$g_1$}      (y)
      (y) edge node[auto] {$\delta_1$} (z)
      (z) edge node[auto] {$f_0$}      (u);

\node[rotate=180] at (0,0) {\Huge$\circlearrowright$};

\end{tikzpicture}
]
\end{document}

CarLaTeX · Answer 2 · 2023-12-10T10:03:12.473

6

This is a job for tikz-cd.

I didn't use \circlearrowright because its tip is different from -latex one.
I drew a circle arrow, this way you can customize it as you wish (arrow tip, position, dimension).

\documentclass{article}
\usepackage{tikz-cd}
\usetikzlibrary{arrows.meta, bending}
\tikzcdset{
    arrow style=tikz,
    arrows={>={latex}},
}
\begin{document}
% code for centering the circle arrow taken from https://tex.stackexchange.com/a/66219/101651
[
\begin{tikzcd}[
  every matrix/.append style={name=mycd},
  execute at end picture={\draw-{latex[flex']} arc (230:-45:6mm);}
  ]
    &[-33pt] H^0(G,A)\ar[r,"f_0"] &[13pt] H^0(G,B)\ar[rd,"g_0"]&[-33pt]\[40pt]
    H^1(G,C)\ar[ur,"\delta_1"] &&& H^0(G,C)\ar[ld,"\delta_0"]\[40pt]
    & H^1(G,B)\ar[ul,"g_1"] & H^1(G,A)\ar[l,"f_1"]
\end{tikzcd}
]
\end{document}

edited Dec 10 '23 at 10:03

answered Dec 10 '23 at 09:24

CarLaTeX

62,716

I cannot compile it in my overleaf. Circle arrow should occurred error. How can I manage it ? – BrauerManinobstruction Dec 10 '23 at 09:51
@BrauerManinobstruction Did you add \usetikzlibrary{arrows.meta, bending} in your preamble? – CarLaTeX Dec 10 '23 at 10:02
@BrauerManinobstruction Also the other definitions I put in my preamble. – CarLaTeX Dec 10 '23 at 10:04
@BrauerManinobstruction In Overleaf my code works, see here https://www.overleaf.com/read/thgbgpxxzkkx#025537 – CarLaTeX Dec 10 '23 at 10:06

score 3 · Answer 3 · answered Dec 10 '23 at 10:20

Variation of nice @Mico answer (+1) with use of quotes library and drawn circle arrow in the middle of hexagon:

\documentclass{article}
\usepackage{tikz,amssymb}
\usetikzlibrary{quotes}
\begin{document}
    [
\begin{tikzpicture}[
        >=latex,
everyy edge quotes/.style = {auto, font=\fontsize}
                    ]
\def\radius{3.3cm} % choose an appropriate value
\node (n1) at (120:\radius) {$H^0(G,A)$};
\node (n2) at ( 60:\radius) {$H^0(G,B)$};
\node (n3) at (  0:\radius) {$H^0(G,C)$};
\node (n4) at (300:\radius) {$H^1(G,A)$};
\node (n5) at (240:\radius) {$H^1(G,B)$};
\node (n6) at (180:\radius) {$H^1(G,C)$};
\path[->]
      (n1) edge["$f_0$"]      (n2)
      (n2) edge["$g_0$"]      (n3)
      (n3) edge["$\delta_0$"] (n4)
      (n4) edge["$f_1$"]      (n5)
      (n5) edge["$g_1$"]      (n6)
      (n6) edge["$\delta_1$"] (n1);
\draw[->] (240:1.2) arc (240:-60:1.2);
\end{tikzpicture}
    ]
\end{document}

score 0 · Answer 4 · answered Feb 28 '24 at 18:12

Here is an option using chains.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary {chains}
\newcommand{\radius}{3}
\begin{document}
[\begin{tikzpicture}[>=latex, start chain=herbrand placed {at=(180-60*\tikzchaincount:\radius)}]
    \foreach \H in {{H^0(G,A)},{H^0(G,B)},{H^1(G,C)},{H^1(G,A)},{H^1(G,B)},{H^0(G,C)}}
        {\node [on chain] {$\H$};}
    \foreach \L[count=\n, evaluate=\n as \m using {int(mod(\n,6)+1)}] in {f_0,g_0,\delta_0,f_1,g_1,\delta_1}
        {\draw[->] (herbrand-\n) to[edge label=$\L$] (herbrand-\m);}
    \draw[->] (270:.5)arc(270:-45:.5);
\end{tikzpicture}]
\end{document}

Hexagon commutative diagram in mathematics (Herbrand quotient diagram)

4 Answers4