forgetful functor from abelian groups to groups
- notation: : →
- Source: category of abelian groups
- Target: category of groups
- Left adjoint:
- 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 initial objects
- preserves coequalizers
- is finitary
Deduced properties
- is continuous
- is conservative
- is essentially injective
- is faithful
- preserves reflexive coequalizers
- preserves epimorphisms
- is cofinitary
- is left exact
- preserves products
- is monadic
- preserves finite products
- preserves equalizers
- preserves monomorphisms
- preserves terminal objects
- preserves coreflexive equalizers
Unsatisfied Properties
Assigned properties
- does not preserve finite coproducts
- is not representable
Deduced properties*
- does not preserve coproducts
- is not right exact
- is not exact
- is not cocontinuous
- is not a left adjoint
- is not comonadic
- is not an equivalence
- is not essentially surjective
*This also uses the deduced satisfied properties.
Unknown properties
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