# Definition:Category of Modules

## 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