Restriction of Scalars - Interpretation As A Functor

Interpretation As A Functor

Restriction of scalars can be viewed as a functor from -modules to -modules. An -homomorphism automatically becomes an -homomorphism between the restrictions of and . Indeed, if and, then

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As a functor, restriction of scalars is the right adjoint of the extension of scalars functor.

If is the ring of integers, then this is just the forgetful functor from modules to abelian groups.