Definition:Category of Left Modules
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Definition
Let $R$ be a ring.
The category of left $R$-modules is the category $\mathbf {R-Mod}$ with:
| Objects: | left modules over $R$ | |
| Morphisms: | left $R$-module homomorphisms | |
| Composition: | composition of mappings | |
| Identity morphisms: | identity mappings |