forgetful functor for rings
- notation: : →
- Source: category of rings
- Target: category of sets
- Related functors: , ,
- nLab Link
This functor maps a ring to its underlying set .
Satisfied Properties
Assigned properties
Deduced properties
Unsatisfied Properties
Assigned properties
- is not essentially injective
- is not essentially surjective
- does not preserve epimorphisms
- does not preserve initial objects
- does not preserve coequalizers
Deduced properties*
- is not an equivalence
- is not full
- is not left-invertible
- does not preserve finite coproducts
- is not right exact
- is not exact
- is not cocontinuous
- does not preserve coproducts
- is not a left adjoint
- is not comonadic
*This also uses the deduced satisfied properties.
Unknown properties
—