tensor multifunctor
1. Definition / Proposition
Let \(R\) be a commutative ring and \(\mathrm{RMod}\) the category RMod. Then for a small discrete diagram \(I\) and the product category \(\prod_{i \in I} \mathrm{RMod}\), the tensor multifunctor is defined as
\begin{align*} \bigotimes_{i \in I}: \prod_{i \in I} \mathrm{Rmod} \rightarrow& \mathrm{RMod} \\ \prod_{i \in I} M_i \mapsto& \bigotimes_{i \in I} M_i \\ ... \end{align*}