With the following code
\documentclass{standalone}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
\arrow[loop left]{l}{\mathrm{id}_A} \ar{r}A &
B\times C \arrow[loop right]{r}{\mathrm{id}_{B\times C}}
\end{tikzcd}
\end{document}
I get:
I'd like to fix the arrows, so that they have the same size independent of the source object, with preference given to the big arrow.
My attempts so far had been only somehow not very effective:
\documentclass{standalone}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
\arrow[loop left]{l}{\mathrm{id}_A} \ar{r}A \hspace{.5cm}&
{B\times C\arrow[loop right]{r}{\mathrm{id}_{B\times C}} }
\end{tikzcd}
\begin{tikzcd}
\arrow[loop left]{l}{\mathrm{id}_A} \ar{r}A &
\hspace{-.7cm}{B\times \hspace{-1.9cm}}& {C\arrow[loop right]{r}{\mathrm{id}_{B\times C}} }
\end{tikzcd}
\end{document}