forgetful functor from abelian groups to groups
- notation:
- Source: category of abelian groups
- Target: category of groups
- Left adjoint functor:
- Related functors: ,
- nLab Link
This functor maps an abelian group to itself, considered merely as a group.
Satisfied Properties
Assigned properties
- is full
- is a right adjoint
- is left-invertible
- preserves coequalizers
- is finitary
Deduced properties
- is continuous
- is conservative
- is essentially injective
- is faithful
- preserves reflexive coequalizers
- preserves regular epimorphisms
- is cofinitary
- is left exact
- preserves products
- is fully faithful
- is full on isomorphisms
- is monadic
- preserves epimorphisms
- preserves finite products
- preserves equalizers
- preserves monomorphisms
- is regular
- is pseudomonic
- preserves binary products
- preserves terminal objects
- preserves coreflexive equalizers
- preserves regular monomorphisms
- preserves initial objects
Unsatisfied Properties
Assigned properties
- does not preserve finite coproducts
- is not dominant
Deduced properties*
- is not essentially surjective
- does not preserve coproducts
- does not preserve binary coproducts
- is not right exact
- is not an equivalence
- is not exact
- is not right-invertible
- is not cocontinuous
- is not coregular
- is not a reflector
- is not an isomorphism
- is not a left adjoint
- is not a coreflector
- is not comonadic
- is not representable
*This also uses the deduced satisfied properties.
Unknown properties
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Undistinguishable functors
These functors in the database currently have exactly the same properties as the forgetful functor from abelian groups to groups. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.