inclusion functor from extended natural numbers to ordinal numbers
This is the inclusion map from the partially ordered set (considered as a thin category as usual) into the partially ordered collection , where we map to the ordinal . It is an example of a functor that preserves binary products, but not terminal objects.
Satisfied Properties
Assigned properties
- is fully faithful
- preserves coproducts
- is cofinitary
Deduced properties
- preserves equalizers
- preserves coreflexive equalizers
- preserves binary products
- is faithful
- is full
- is conservative
- preserves monomorphisms
- preserves finite coproducts
- preserves coequalizers
- preserves reflexive coequalizers
- preserves binary coproducts
- preserves epimorphisms
- preserves regular monomorphisms
- is full on isomorphisms
- preserves initial objects
- is cocontinuous
- is right exact
- preserves regular epimorphisms
- is essentially injective
- is pseudomonic
- is a left adjoint
- is finitary
- is coregular
- is comonadic
- is left-invertible
Unsatisfied Properties
Assigned properties
- does not preserve terminal objects
Deduced properties*
- is not a reflector
- does not preserve finite products
- is not an equivalence
- does not preserve products
- is not left exact
- is not essentially surjective
- is not right-invertible
- is not an isomorphism
- is not continuous
- is not exact
- is not regular
- is not a right adjoint
- is not representable
- is not dominant
- is not a coreflector
- is not monadic
*This also uses the deduced satisfied properties.
Unknown properties
—