abelianization functor for groups

 algebra  free
Notation (−)ab:Grp→Ab(-)^{\ab}: \Grp \to \Ab Domain category of groupsCodomain category of abelian groupsRight adjoint forgetful functor from abelian groups to groups External nLab Link

This functor maps a group GG to its abelianization Gab≔G/[G,G]G^{\ab} \coloneqq G/[G,G].

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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Indistinguishable functors

These functors in the database currently have exactly the same properties as the abelianization functor for groups. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.