forgetful functor from commutative rings to rings
This is the inclusion functor that maps a commutative ring to itself, regarded merely as a ring.
Satisfied properties
Assigned properties
- is fully faithful
- is a right adjoint
- preserves initial objects
- is finitary
- preserves coequalizers
- preserves epimorphisms
Deduced properties
- is continuous
- is faithful
- is full
- is conservative
- is left-invertible
- is monadic
- preserves reflexive coequalizers
- preserves regular epimorphisms
- is cofinitary
- is left exact
- preserves products
- is essentially injective
- is full on isomorphisms
- preserves finite products
- preserves equalizers
- preserves monomorphisms
- is regular
- is pseudomonic
- preserves binary products
- preserves terminal objects
- preserves coreflexive equalizers
- preserves regular monomorphisms
Unsatisfied properties
Assigned properties
- is not dominant
- does not preserve binary coproducts
Deduced properties*
- is not essentially surjective
- does not preserve finite coproducts
- is not an equivalence
- is not right-invertible
- does not preserve coproducts
- is not right exact
- is not a reflector
- is not an isomorphism
- is not exact
- is not a coreflector
- is not cocontinuous
- is not coregular
- is not a left adjoint
- is not comonadic
- is not representable
*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 forgetful functor from commutative rings to rings. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.