forgetful functor from Hausdorff spaces to topological spaces
This is the inclusion functor that maps a Hausdorff space to itself. It can also be viewed as a forgetful functor, since Hausdorff spaces "forget" that they are Hausdorff.
Satisfied properties
Assigned properties
- is fully faithful
- is a right adjoint
- preserves coproducts
- preserves regular epimorphisms
Deduced properties
- is continuous
- is faithful
- is full
- is conservative
- is left-invertible
- is monadic
- preserves finite coproducts
- is cofinitary
- is left exact
- preserves products
- is essentially injective
- is full on isomorphisms
- preserves binary coproducts
- preserves initial objects
- preserves finite products
- preserves equalizers
- preserves monomorphisms
- is regular
- is pseudomonic
- preserves binary products
- preserves terminal objects
- preserves coreflexive equalizers
- preserves regular monomorphisms
Unsatisfied properties
Assigned properties
- does not preserve epimorphisms
- is not dominant
- is not finitary
Deduced properties*
- is not essentially surjective
- is not cocontinuous
- is not right exact
- is not an equivalence
- is not exact
- is not right-invertible
- is not a left adjoint
- does not preserve coequalizers
- is not coregular
- is not a reflector
- is not an isomorphism
- is not a coreflector
- does not preserve reflexive coequalizers
- is not comonadic
- is not representable
*This also uses the deduced satisfied properties.
Unknown properties
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