forgetful functor from torsion-free abelian groups to abelian groups

 algebra  forgetful
Notation UTorsFreeAb,Ab:TorsFreeAb→AbU_{\TorsFreeAb, \Ab}: \TorsFreeAb \to \Ab Domain category of torsion-free abelian groupsCodomain category of abelian groups Related UAb,GrpU_{\Ab,\Grp}, UGrp,MonU_{\Grp,\Mon}, UTorsAb,AbU_{\TorsAb, \Ab}
This is the inclusion functor TorsFreeAb↪Ab\TorsFreeAb \hookrightarrow \Ab. It can also be seen as a forgetful functor which forgets the property of being torsion-free. The functor provides a typical example of a fully faithful functor that does not preserve coequalizers and does not preserve epimorphisms.

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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