forgetful functor for rings

Satisfied Properties

Assigned properties

• is representable
• is monadic
• is finitary
• preserves reflexive coequalizers

Deduced properties

• is a right adjoint
• is continuous
• is conservative
• is faithful
• preserves regular epimorphisms
• is cofinitary
• is left exact
• preserves products
• preserves finite products
• preserves equalizers
• preserves monomorphisms
• is regular
• preserves binary products
• preserves terminal objects
• preserves coreflexive equalizers
• preserves regular monomorphisms

Unsatisfied Properties

Assigned properties

• is not essentially injective
• is not dominant
• does not preserve epimorphisms
• does not preserve initial objects
• does not preserve coequalizers

Deduced properties*

• is not left-invertible
• is not full on isomorphisms
• is not essentially surjective
• is not a coreflector
• does not preserve finite coproducts
• is not right exact
• does not preserve binary coproducts
• is not an equivalence
• is not exact
• is not right-invertible
• is not full
• is not pseudomonic
• is not fully faithful
• is not cocontinuous
• does not preserve coproducts
• is not coregular
• is not a reflector
• is not an isomorphism
• is not a left adjoint
• is not comonadic

*This also uses the deduced satisfied properties.