Increase the space around \circ in script style

Question

Is there some way to increase the horizontal space around \circ when it is in script style? For example, the label over the arrows in a commutative diagram is often put in script style, and left almost no extra space around \circ:

This usually won't be a big problem, but in some cases the labels look quite ugly (for example, the vertical labels in the following diagram):

I wonder if there is some way to have the normal thin space around \circ as in text or display mode?

Below is a MWE to play with.

\documentclass{article}

\usepackage{tikz-cd}

\begin{document}

\begin{tikzcd}
    \bullet & \bullet
    \arrow["a \circ a",from=1-1, to=1-2]
\end{tikzcd}

\( a \circ a \)

\( \scriptstyle a \circ a \)

\end{document}

Answer 1

I'm not sure you can coerce tikz-cd to apply this to all labels, but it works with the explicit command.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz-cd}

\newcommand{\cdl}[1]{\text{$\medmuskip=0.6\medmuskip#1$}}

\begin{document}

\begin{tikzcd}
\bullet \arrow[r,"\cdl{a\circ a}"] & \bullet \\
\bullet \arrow[r,"a\circ a"] & \bullet
\end{tikzcd}

\end{document}

I reduced \medmuskip because the standard value seems too large in this case.

Why does this work? Because \text appears in \scriptstyle, so it uses \sf@size inside it, but math is in text style.

I believe that in LuaTeX you can change the behavior that in script style no space around binary operation symbols is added.