Box around tikz-cd

Question

About this code, I'd like to create two boxes around these tikz-cds. Is it possible? Thank you so much. The code:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[a4paper,top=3cm,bottom=3cm,left=1.5cm,right=1.5cm]{geometry}
\usepackage{tikz}
\usepackage{tikz-cd}
\usepackage{stix}
\usepackage[bb=ams]{mathalpha}
\usepackage{mathtools}
\newcommand{\tonde}[1]{\bigl(#1\bigr)}
\newcommand{\R}{\mathbb R}
\newcommand{\A}{\mathbb A}
\title{TikZ - tikzsets}
\author{PUCK}
\date{November 2022}
\begin{document}
\maketitle
\Large
\section{Introduction}
\begin{equation}
\begin{tikzcd}[arrow style=tikz, >={Triangle[length=2mm]}, cells={nodes={inner sep=2mm}}, row sep=1.25cm,column sep=2cm]
M\arrow[r, "f\in C^\infty"] & N \ g\tonde{U} \arrow[u, hook, "i_M"] \arrow[r, "\bar{f}\in C^\infty"] & h\tonde{V}\arrow[u, hook, "i_N"']\U\arrow[u, hook, two heads, "g", "\eqqsim"'] \arrow[r, hook, two heads, "\phi\coloneqq h^{-1}\circ f\circ g","\eqqsim"'] &V\arrow[u, hook, "h"', "\eqqsim"]
\end{tikzcd}\implies
\begin{tikzcd}[arrow style=tikz, >={Triangle[length=2mm]}, cells={nodes={inner sep=2mm}}, row sep=1.5cm, column sep=2cm]
\textbf{T}_xM\subset\R^k\arrow[r, "df_x"] & \textbf{T}_yN \subset\R^l\\textbf{T}_uU=\R\A^m\arrow[r, "d\phi_u"'] \arrow[u, "dg_u"] & \textbf{T}_vV=\R\A^n \arrow[u, "dh_v"']
\end{tikzcd}
\end{equation}
\end{document}

Answer 1

Like this?

Edit:
Deleted is use of preview package which is used to see only equation with tikzcd diagrams. It seems that this trick is not known to OP, so it is better to remove it. Now compilation result is seen on top of whole page. Hopefully that now proposed solutions are more clear.

Rectangles are draw as fit nodes in execute at end picture:

\documentclass{article}
\usepackage{stix}
\usepackage[bb=ams]{mathalpha}
\usepackage{mathtools}
\newcommand{\R}{\mathbb R}
\newcommand{\A}{\mathbb A}
\usepackage{tikz-cd}
\usetikzlibrary{arrows.meta,
                fit,
                patterns.meta}
\tikzcdset{
arrow style=tikz, 
>={Triangle[length=2mm]}, 
cells={nodes={inner sep=2mm}},
        }
\tikzset{
every matrix/.append style = {name=m},
F/.style = {draw=red, very thick, rounded corners, inner sep=5pt, fit=#1}
        }
\begin{document}
\begin{equation}
    \begin{tikzcd}[column sep=24mm, row sep=12mm,
execute at end picture = { % <----
    \node[F = (m-1-1) (m-3-2) ] {};
                        }% end of execute at end picture
                    ]
M \rar["f\in C^\infty"] & N     \ 
g(U) \uar[hook, "i_M"] \rar["\bar{f}\in C^\infty"] 
                        & h(V)\uar[hook, "i_N"']   \
U \uar[hook, two heads, "g", "\eqqsim"'] 
  \rar[hook, two heads, "\phi\coloneqq h^{-1}\circ f\circ g","\eqqsim"'] 
                        & V \uar[hook, "h"', "\eqqsim"]
    \end{tikzcd}
  \implies
    \begin{tikzcd}[sep=12mm,
execute at end picture = {% <----
    \node[F = (m-1-1) (m-2-2) ] {};
                        }% end of execute at end picture
                    ]
\textbf{T}_xM\subset\R^k \rar["df_x"] 
                        & \textbf{T}_yN \subset\R^l \
\textbf{T}_uU=\R\A^m \rar["d\phi_u"'] 
                     \uar["dg_u"] 
                        & \textbf{T}_vV=\R\A^n \uar["dh_v"']
    \end{tikzcd}
\end{equation}
\end{document}

Addendum:

• Without defining common \tikzset for node style. Style is now defined in node.
• Naming of matrix by every matrix/.append style = {name=m} is replaced by use of tikz@f@... for diagram name:

\documentclass{article}
\usepackage{stix}
\usepackage[bb=ams]{mathalpha}
\usepackage{mathtools}
\newcommand{\R}{\mathbb R}
\newcommand{\A}{\mathbb A}
\usepackage{tikz-cd}
\usetikzlibrary{arrows.meta,
                fit,
                patterns.meta}
\tikzcdset{
arrow style=tikz,
>={Triangle[length=2mm]},
          }
\begin{document}
\begin{preview}
\begin{equation}
    \begin{tikzcd}[column sep=24mm, row sep=12mm,
execute at end picture = { % <----
    \node[draw=red, very thick, rounded corners, fit=(tikz@f@1)] {}; % first diagram
                        }% end of execute at end picture
                    ]
M \rar["f\in C^\infty"] & N     \
g(U) \uar[hook, "i_M"] \rar["\bar{f}\in C^\infty"]
                        & h(V)\uar[hook, "i_N"']   \
U \uar[hook, two heads, "g", "\eqqsim"']
  \rar[hook, two heads, "\phi\coloneqq h^{-1}\circ f\circ g","\eqqsim"']
                        & V \uar[hook, "h"', "\eqqsim"]
    \end{tikzcd}
  \implies
    \begin{tikzcd}[sep=12mm,
execute at end picture = {% <----
    \node[draw=red, very thick, rounded corners, fit=(tikz@f@2)] {}; % second diagram
                         }% end of execute at end picture
                  ]
\mathbf{T}_xM\subset\R^k \rar["df_x"]
                        & \mathbf{T}_yN \subset\R^l \
\mathbf{T}_uU=\R\A^m \rar["d\phi_u"']
                     \uar["dg_u"]
                        & \mathbf{T}_vV=\R\A^n \uar["dh_v"']
    \end{tikzcd}
\end{equation}
\end{preview}
\end{document}

• As suggested @Qrrbrbirlbel in his comment, name of diagram as \tikzcdmatrixname is available at the end of the diagram (when execute at end picture is executed. So nodes code can be changed to:

...
    \begin{tikzcd}[...,
execute at end picture = {% <---- at each tikzcd diagram
    \node[draw=red, very thick, rounded corners, fit=(\tikzcdmatrixname)] {};
                         }% end of execute at end picture
...

Compilation result is similar as before:

Answer 2

You can use the backgrounds library library to draw a rectangular box around the whole diagram. See the manual for more options on how to change the outcome of that rectangle, mostly the settings on inner frame seps.

I've also

• used \DeclarePairedDelimiter from mathtools to define \tonde.

  Now you can use \tonde*{<stuff>} and the parentheses are scaled automatically but you can also do \tonde[\big]{<stuff>} and \bigl(<stuff>\bigr) will be typeset. (For a single V there's no need to use \big?.)

• defined a my CD style for repeated settings for your diagram. If you want all your diagrams to have these options you can just append these options to every diagram:

  \tikzcdset{every diagram/.append style={…}}
  

• used \mathbf instead of \textbf.

• and defined a \diff for the differential d (and commented out the version for an upright d).

The amsmath package also provides a \boxed macro that could be used here but doesn't the whole functionality that TikZ brings.

Code

\documentclass{article}
\usepackage[a4paper,top=3cm,bottom=3cm,left=1.5cm,right=1.5cm]{geometry}
\usepackage{tikz-cd}
\usepackage{stix}
\usepackage[bb=ams]{mathalpha}
\usepackage{mathtools}
\newcommand{\R}{\mathbb R}
\newcommand{\A}{\mathbb A}
\DeclarePairedDelimiter{\tonde}() % better then your own \tonde
\newcommand{\diff}{d}            % diff d italic
%\newcommand{\diff}{\mathup{d}}   % diff d upright
\usetikzlibrary{backgrounds}      % for background rectangle
\tikzcdset{
  my CD/.style={                  % shortcut for repeated style
    arrow style=tikz,
    >={Triangle[length=2mm]},
    cells={nodes={inner sep=2mm}},
    row sep=1.25cm,  column sep=2cm}}
\tikzset{
  boxed/.style={

    show background rectangle,    % adds a box around the whole picture
    background rectangle/.append style={ % that is red, thick and rounded
      draw=red, thick, rounded corners}}}
\begin{document}
\Large
\section{Introduction}
\begin{equation}
\begin{tikzcd}[my CD, boxed]
 M              \arrow[r, "f\in C^\infty"] & N \
 g\tonde{U}     \arrow[u, hook, "i_M"]
                \arrow[r, "\bar{f}\in C^\infty"]
   & h\tonde{V} \arrow[u, hook, "i_N"'] \
 U              \arrow[u, hook, two heads, "g", "\eqqsim"']
                \arrow[r, hook, two heads,
                       "\phi\coloneqq h^{-1}\circ f\circ g", "\eqqsim"']
   & V          \arrow[u, hook, "h"', "\eqqsim"]
\end{tikzcd}
\implies
\begin{tikzcd}[my CD, boxed]
 \mathbf{T}_xM \subset\R^k    \arrow[r, "\diff f_x"    ]
   & \mathbf{T}_yN \subset\R^l \
 \mathbf{T}_uU=\R\A^m         \arrow[r, "\diff \phi_u"']
                              \arrow[u, "\diff g_u"    ]
   & \mathbf{T}_vV=\R\A^n     \arrow[u, "\diff h_v"'   ]
\end{tikzcd}
\end{equation}
\end{document}

Output

Answer 3

I suggest appending a style to the matrix (the CD is a TikZ matrix), for convenience I created mymatr style (updated according to Qrrbrbirlbel's advice):

\documentclass{article}
%\usepackage[utf8]{inputenc} no more needed in up-to-date distributions: https://tex.stackexchange.com/a/370279/101651
\usepackage[a4paper,top=3cm,bottom=3cm,left=1.5cm,right=1.5cm]{geometry}
%\usepackage{tikz} not needed, tikz-cd already load it
\usepackage{tikz-cd}
\tikzset{mymatr/.style={every outer matrix/.append style={draw=red, inner xsep=4pt , inner ysep=6pt, rounded corners, very thick}}}
\usepackage{stix}
\usepackage[bb=ams]{mathalpha}
\usepackage{mathtools}
\newcommand{\tonde}[1]{\bigl(#1\bigr)}
\newcommand{\R}{\mathbb R}
\newcommand{\A}{\mathbb A}
\title{TikZ - tikzsets}
\author{PUCK}
\date{November 2022}
\begin{document}
\maketitle
\Large
\section{Introduction}
\begin{equation}
\begin{tikzcd}[mymatr, 
arrow style=tikz, >={Triangle[length=2mm]}, cells={nodes={inner sep=2mm}}, row sep=1.25cm,column sep=2cm]
M\arrow[r, "f\in C^\infty"] & N \ g\tonde{U} \arrow[u, hook, "i_M"] \arrow[r, "\bar{f}\in C^\infty"] & h\tonde{V}\arrow[u, hook, "i_N"']\U\arrow[u, hook, two heads, "g", "\eqqsim"'] \arrow[r, hook, two heads, "\phi\coloneqq h^{-1}\circ f\circ g","\eqqsim"'] &V\arrow[u, hook, "h"', "\eqqsim"]
\end{tikzcd}\implies
\begin{tikzcd}[mymatr,

arrow style=tikz, >={Triangle[length=2mm]}, cells={nodes={inner sep=2mm}}, row sep=1.5cm, column sep=2cm]
\textbf{T}_xM\subset\R^k\arrow[r, "df_x"] & \textbf{T}_yN \subset\R^l\\textbf{T}_uU=\R\A^m\arrow[r, "d\phi_u"'] \arrow[u, "dg_u"] & \textbf{T}_vV=\R\A^n \arrow[u, "dh_v"']
\end{tikzcd}
\end{equation}
\end{document}