Tensor product

The tensor product is a bifunctor in the category of modules over a fixed ring $R$. In the subcategory of algebras over $R$, the tensor product is just the cofibered product over $R$.

Definition

The tensor product of two $R$-modules $M$ and $M'$, denoted by Failed to parse (unknown function "\tensor"): {\displaystyle M\tensor_R M'} , is an $R-module$ $T$ satisfying the universal property