forgetful functor from finite abelian groups to abelian groups

 algebra  forgetful
Notation UFinAb,Ab:FinAb→AbU_{\FinAb, \Ab}: \FinAb \to \Ab Domain category of finite abelian groupsCodomain category of abelian groups Related UFinGrp,GrpU_{\FinGrp, \Grp}, UTorsAb,AbU_{\TorsAb, \Ab} External nLab Link

This is the inclusion functor FinAb↪Ab\FinAb \hookrightarrow \Ab that maps a finite abelian group to itself, regarded as an abelian group that has "forgotten" that it is finite. It provides an example of a fully faithful functor that is neither finitary nor cofinitary.

Satisfied Properties

Assigned properties

Deduced properties

Unsatisfied Properties

Assigned properties

Deduced properties*

*This also uses the deduced satisfied properties.

Unknown properties

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