forgetful functor from torsion abelian groups to abelian groups
- Notation:
- Domain: category of torsion abelian groups
- Codomain: category of abelian groups
- Related functors: , ,
- nLab Link
This is the inclusion functor . It can also be viewed as a forgetful functor that forgets the property of being torsion. It is a typical example of a fully faithful functor that preserves finite products but does not preserve infinite products.
Satisfied Properties
Assigned properties
- is fully faithful
- is left exact
- is a left adjoint
Deduced properties
- preserves equalizers
- preserves finite products
- preserves monomorphisms
- is faithful
- is full
- is conservative
- is cocontinuous
- is comonadic
- is left-invertible
- preserves binary products
- preserves terminal objects
- preserves coreflexive equalizers
- preserves regular monomorphisms
- preserves finite coproducts
- is essentially injective
- is full on isomorphisms
- is finitary
- preserves coproducts
- is right exact
- is exact
- preserves initial objects
- is pseudomonic
- preserves binary coproducts
- preserves coequalizers
- preserves epimorphisms
- is coregular
- preserves reflexive coequalizers
- preserves regular epimorphisms
- is regular
Unsatisfied Properties
Assigned properties
Deduced properties*
- is not continuous
- is not cofinitary
- is not essentially surjective
- is not a right adjoint
- is not an equivalence
- is not representable
- is not right-invertible
- is not a reflector
- is not an isomorphism
- is not monadic
- is not a coreflector
*This also uses the deduced satisfied properties.
Unknown properties
—
Indistinguishable functors
These functors in the database currently have exactly the same properties as the forgetful functor from torsion abelian groups to abelian groups. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.