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One makes sure In order to have use it, download the the file <code>tikzlibrarycd.code.tex</code>, and follows put it in <code>CONTEXT_HOME/tex/texmf-modules/tex/generic/pgf/libraries/</code>. Then run<pre>mtxrun --generatecontext --make</pre>You should now be able to use tikz-cd. Makes sure to follow the translation rules in the manual for ConTeXt. In addition to that, one it seems to that you have to replace the apostrophe with "below".
Edited the Commutative Diagrams section for more clarity
There is a tikz-cd package at CTAN: https://www.ctan.org/tex-archive/graphics/pgf/contrib/tikz-cd?lang=en
The first few examples in the manual, which compiled with latest ConTeXt:
