forgetful functor from finite abelian groups to abelian groups
- Notation:
- Domain: category of finite abelian groups
- Codomain: category of abelian groups
- Related functors: ,
- nLab Link
This is the inclusion functor that maps a finite abelian group to itself, regarded as an abelian group that has "forgotten" that it is finite. It provides an example of a fully faithful functor that is neither finitary nor cofinitary.
Satisfied Properties
Assigned properties
- is fully faithful
- is exact
- preserves products
- preserves coproducts
Deduced properties
- preserves finite products
- is left exact
- is right exact
- is faithful
- is full
- is conservative
- preserves finite coproducts
- preserves binary products
- preserves terminal objects
- preserves equalizers
- preserves monomorphisms
- is full on isomorphisms
- preserves binary coproducts
- preserves initial objects
- preserves coequalizers
- preserves epimorphisms
- preserves coreflexive equalizers
- preserves regular monomorphisms
- is essentially injective
- is pseudomonic
- preserves reflexive coequalizers
- preserves regular epimorphisms
- is regular
- is coregular
Unsatisfied Properties
Assigned properties
- is not dominant
- is not finitary
- is not cofinitary
- is not left-invertible
Deduced properties*
- is not an equivalence
- is not continuous
- is not essentially surjective
- is not a right adjoint
- is not cocontinuous
- is not a left adjoint
- is not a reflector
- is not an isomorphism
- is not representable
- is not right-invertible
- is not monadic
- is not a coreflector
- is not comonadic
*This also uses the deduced satisfied properties.
Unknown properties
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