free group functor

 algebra  free
Notation FGrp:Set→GrpF_{\Grp}: \Set \to \Grp Domain category of setsCodomain category of groupsRight adjoint forgetful functor for groups Related Z[−]\IZ[-], FMon,GrpF_{\Mon,\Grp} External nLab link
This functor maps a set XX to the free group FGrp(X)F_{\Grp}(X) on that set. In the proofs, we abbreviate F≔FGrpF \coloneqq F_{\Grp}.

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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