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