The following code:


A\times B       &C\\\

([g,\alpha], [f,\sigma])\ar[mapsto]{r}              & [hf,\mu\alpha]


give the error

"! Package pgf Error: No shape named tikz@f@125-2-2 is known."

I suspect that is for the [] in the place 2-2 but I don't know whay I couldn't use it.

What should I do if I want to use [ ] like that?


You have to set the lower right term in braces. It seems as if tikz-cd does not understand the [] here. Maybe this character is active here. As tikz-cd does not find something in the cell 2-2 but you are pointing an arrow towards there, you are getting the error you have posted.

% arara: pdflatex


    A\times B & C \\    
    ([g,\alpha], [f,\sigma])\ar[mapsto]{r} & {[hf,\mu\alpha]}   

enter image description here

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