New answers tagged noncommutative-geometry
The term you want is "distributes over," not "commutes with." (Whatever "$A$ commutes with $B$" means it should be symmetric in $A$ and $B$, which the condition you want is not.) Such monoidal categories are called distributive. Examples include any closed monoidal category with coproducts because in this case $A \otimes (-)$ has a right adjoint and hence ...
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