\begin{definition}[Definition:Category of Left Modules]
Let $R$ be a ring.
The '''category of left $R$-modules''' is the category $\mathbf {R-Mod}$ with:
{{DefineCategory
| ob = left modules over $R$
| mor = left $R$-module homomorphisms
| id = identity mappings
| comp = composition of mappings
}}
\end{definition}