forgetful functor from rings to monoids

 algebra  forgetful
Notation URing,Mon:Ring→MonU_{\Ring,\Mon}: \Ring \to \Mon Domain category of ringsCodomain category of monoidsLeft adjoint monoid ring functor Related URingU_{\Ring} External nLab link
This functor maps a ring to its underlying multiplicative monoid, which has "forgotten" the addition of the ring.

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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