I have recently [asked a question](https://mathoverflow.net/questions/332874/quantum-scattering-experiments-c-modules-n-modules-and-their-monads) about the composition of two monads, namely $\mathcal{M}_P = \mathcal{M}_C \cdot \mathcal{M}_C$.  I am conjecturing that the cateogory of $\mathbb{C}$-Modules and the category of $\mathbb{N}$-Modules also live in a category of categories, namely a category of categories of modules, $\mathcal{C}_{Mod}$.  Since the monads compose, I am guessing that the modules themselves compose in the category $\mathcal{C}_{Mod}$.  We should, then, expect some kind of composition in this category.  A first guess is that of a tensor product, and I have just read somewhere that there is a tensor product of modules.  What is the standard name for the inducement where a composition of monads induces a tensor product of modules?