Wie kann ich TikZ-Stile kombinieren oder vererben?

Man kann einen bereits definierten Stil einfach in die nächste Definition aufnehmen:

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\tikzset{math/.style={execute at begin node=$, execute at end node=$}}
\tikzset{boldmath/.style={math,font=\boldmath}}
 
 
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Oder etwas feiner, und in einem \tikzset zusammengefasst:

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\tikzset{%
  math/.style={execute at begin node=$, execute at end node=$},
  bold/.style={font=\boldmath},
  boldmath/.style={bold,math}
}
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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Weitergetrieben für kleine, rote und mathematische Knoten und als Komplettbeispiel zum Probieren, basierend auf dem Code Deiner oben verlinkten Frage:

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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning}
\newcommand*{\mal}{\mathbin{\raisebox{0.4ex}{\scriptsize$\otimes$}}}
\tikzset{%
  red/.style={color=red},
  math/.style={execute at begin node=$, execute at end node=$},
  boldmath/.style={math,font=\boldmath},
  small/.style={font=\small},
  smallmath/.style={math,small},
  redsmallmath/.style={red,small,math}
}
\begin{document}
\begin{tikzpicture}[node distance=3em]
  \node[math] (A) {A^2};
  \node[boldmath] [base right = of A] (AxA) {A\mal A};
  \draw (A.east |- AxA) edge [->] node [above,redsmallmath] {\scriptstyle\varphi} (AxA);
\end{tikzpicture}
\end{document}
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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Das hat dann eher in sehr komplexen Diagrammen mit verschiedenen Beschriftungstypen Vorteile.