Stone-Čech compactification functor
This is the functor that is left adjoint to the inclusion functor . There are various constructions (see Wikipedia), one being that is the closure of the image of the canonical map Among other things, this functor provides an example of a reflector that does not preserve binary products.
Satisfied properties
Assigned properties
- is a reflector
Deduced properties
- is a left adjoint
- is right-invertible
- preserves terminal objects
- is essentially surjective
- is cocontinuous
- is dominant
- is finitary
- preserves coproducts
- is right exact
- preserves finite coproducts
- preserves coequalizers
- preserves epimorphisms
- preserves binary coproducts
- preserves initial objects
- preserves reflexive coequalizers
- preserves regular epimorphisms
Unsatisfied properties
Assigned properties
- is not essentially injective
- is not faithful
- is not full
- does not preserve regular monomorphisms
- is not cofinitary
- does not preserve binary products
Deduced properties*
- is not continuous
- does not preserve finite products
- does not preserve equalizers
- does not preserve monomorphisms
- does not preserve coreflexive equalizers
- is not fully faithful
- is not left-invertible
- is not full on isomorphisms
- is not pseudomonic
- is not monadic
- is not coregular
- is not conservative
- is not comonadic
- is not a right adjoint
- is not an equivalence
- does not preserve products
- is not left exact
- is not representable
- is not an isomorphism
- is not exact
- is not regular
- is not a coreflector
*This also uses the deduced satisfied properties.
Unknown properties
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