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 (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M\tensor_R M'} , is an $R-module$ $T$ satisfying the universal property