How do you draw a commutative diagram inside another commutative diagram in tikz?

Question

I have this commutative diagram to draw :

I have no idea how to get the inner diagram to properly display and not mess with the whole thing. I can get the outer one but as soon as I do anything to try and add the extra arrow and all, I get plenty of errors, and the diagram looks nothing like the picture above (done in geogebra). I'd be grateful if anyone could help out ! Also, I have a less important issue, but is it possible to scale the diagram ? The command \begin{tikzcd}[scale=2] doesn't seem to do anything, and the environnement \scalebox{2}{...} produces errors and doesn't scale anything either. Thanks.

Answer 1

You can just use one diagram for that. (Note that solution adding boxes od width 0 may screw up the bounding box.)

\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}[every arrow/.append style={thick,-stealth},
execute at end picture={
\node[right=-4pt,fill=white,baseline={(aBf.base)}] at (aBf.east){$=\{a'\in\mathcal{B}\mid f(a')=b\}$};}
]
 A \arrow[rrrr,"f"]  \arrow[dddrr,"\pi_{\mathcal{B}_f}"'] & & & & B \\[-1em]
 & a \arrow[rr] \arrow[dr] & & b & \\[2ex]
 && |[alias=aBf]|[a]_{\mathcal{B}_f} \arrow[ur] && \\
 && \mathcal{B}_f \arrow[uuurr,"\bar f"' {pos=0.85}] && \\
\end{tikzcd}
\end{document}

Or a smaller version thereof.

\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}[every arrow/.append style={thick,-stealth},column sep=small,
row sep=small,
execute at end picture={
\node[right=-4pt,fill=white,baseline={(aBf.base)}] at (aBf.east){$=\{a'\in\mathcal{B}\mid f(a')=b\}$};}
]
 A \arrow[rrrr,"f"]  \arrow[dddrr,"\pi_{\mathcal{B}_f}"'] & & & & B \\[-1em]
 & a \arrow[rr] \arrow[dr] & & b & \\[2ex]
 && |[alias=aBf]|[a]_{\mathcal{B}_f} \arrow[ur] && \\
 && \mathcal{B}_f \arrow[uuurr,"\bar f"' {pos=0.85}] && \\
\end{tikzcd}
\end{document}