In algebra, given a ring R {\displaystyle R} , the category of left modules over R {\displaystyle R} is the category whose objects are all left modules over R {\displaystyle R} and whose morphisms are all module homomorphisms between left R {\displaystyle R} -modules. For example, when R {\displaystyle R} is the ring of integers Z {\displaystyle \mathbb {Z} } , it is the same thing as the category of abelian groups.
In algebra, given a ring R {\displaystyle R} , the category of left modules over R {\displaystyle R} is the category whose objects are all left modules over R {\displaystyle R} and whose morphisms are all module homomorphisms between left R {\displaystyle R} -modules. For example, when R {\displaystyle R} is the ring of integers Z {\displaystyle \mathbb {Z} } , it is the same thing as the category of abelian groups.
Source: Wikipedia "Category of modules" · CC BY-SA 4.0
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