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