forgetful functor from finite groups to groups
This is the inclusion functor . It can also be viewed as a forgetful functor that forgets the property of being finite. Among other things, it provides an example of a fully faithful functor that is neither finitary nor cofinitary.
Satisfied Properties
Assigned properties
- is fully faithful
- is left exact
- preserves coequalizers
- preserves products
- preserves coproducts
Deduced properties
- preserves finite products
- preserves equalizers
- preserves monomorphisms
- is faithful
- is full
- is conservative
- preserves finite coproducts
- preserves reflexive coequalizers
- preserves regular epimorphisms
- preserves binary products
- preserves terminal objects
- preserves coreflexive equalizers
- preserves regular monomorphisms
- is regular
- is full on isomorphisms
- preserves binary coproducts
- preserves initial objects
- preserves epimorphisms
- is essentially injective
- is pseudomonic
Unsatisfied Properties
Assigned properties
- is not dominant
- is not left-invertible
- is not finitary
- is not cofinitary
- is not right exact
Deduced properties*
- is not an equivalence
- is not continuous
- is not exact
- is not essentially surjective
- is not a right adjoint
- is not cocontinuous
- is not coregular
- 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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