forgetful functor from finite sets to sets
This functor is the inclusion functor mapping a finite set to itself. It can also be regarded as a forgetful functor since it makes finite sets "forget" their finiteness. The functor is a basic example of a representable functor which is not a right adjoint.
Satisfied Properties
Assigned properties
- is fully faithful
- is representable
- is cocontinuous
Deduced properties
- is continuous
- is faithful
- is full
- is conservative
- is finitary
- preserves coproducts
- is right exact
- is cofinitary
- is left exact
- preserves products
- is full on isomorphisms
- preserves finite coproducts
- preserves coequalizers
- preserves epimorphisms
- preserves finite products
- is exact
- preserves equalizers
- preserves monomorphisms
- is essentially injective
- is pseudomonic
- preserves binary coproducts
- preserves initial objects
- preserves reflexive coequalizers
- preserves regular epimorphisms
- preserves binary products
- preserves terminal objects
- preserves coreflexive equalizers
- preserves regular monomorphisms
- is regular
- is coregular
Unsatisfied Properties
Assigned properties
- is not left-invertible
- is not dominant
Deduced properties*
- is not an equivalence
- is not essentially surjective
- is not a right adjoint
- is not a left adjoint
- is not a reflector
- is not an isomorphism
- is not right-invertible
- is not monadic
- is not a coreflector
- is not comonadic
*This also uses the deduced satisfied properties.
Unknown properties
—