forgetful functor from groups to pointed sets
- notation:
- Source: category of groups
- Target: category of pointed sets
- Related functors: ,
- nLab Link
This functor maps a group to its underlying pointed set , whose base point is the identity element of . It is an example of an essentially surjective functor which is not right-invertible.
Satisfied Properties
Assigned properties
- is a right adjoint
- is conservative
- is finitary
- preserves reflexive coequalizers
- is essentially surjective
Deduced properties
- is continuous
- is dominant
- is monadic
- preserves regular epimorphisms
- is cofinitary
- is left exact
- preserves products
- is faithful
- preserves epimorphisms
- preserves finite products
- preserves equalizers
- preserves monomorphisms
- is regular
- preserves binary products
- preserves terminal objects
- preserves coreflexive equalizers
- preserves regular monomorphisms
- preserves initial objects
Unsatisfied Properties
Assigned properties
- is not essentially injective
- does not preserve coequalizers
- is not right-invertible
Deduced properties*
- is not a reflector
- is not an equivalence
- is not left-invertible
- is not full on isomorphisms
- is not a coreflector
- is not right exact
- does not preserve binary coproducts
- is not fully faithful
- is not an isomorphism
- is not exact
- is not full
- is not pseudomonic
- is not cocontinuous
- does not preserve finite coproducts
- is not coregular
- is not a left adjoint
- does not preserve coproducts
- is not comonadic
- is not representable
*This also uses the deduced satisfied properties.
Unknown properties
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