Definition:Forgetful Functor from Modules to Abelian Groups
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Definition
Let $R$ be a ring.
Let $\mathbf C$ be the category of left modules or category of left modules over $R$.
Let $\mathbf{Ab}$ be the category of abelian groups.
The forgetful functor $\mathbf C \to \mathbf{Ab}$ is the covariant functor with
Object functor: | sends a left module or right module to its underlying abelian group. | |
Morphism functor: | sends a mapping to itself |