Webpage of the Compositional Systems and Methods group at TalTech.

On the tensor product of symmetric monoidal theories

The slogan associated with the tensor product of algebraic theories is that "A model of the tensor product of X and Y is a model of X in the category of models of Y". This is not, strictly speaking, true. I plan to explain why not, and to further explain why the slogan is sort of true after all, all at the level of symmetric strict monoidal categories, since the case of algebraic theories follows easily from this more basic one.