forgetful functor for topological spaces
This functor maps a topological space to its underlying set .
Satisfied Properties
Assigned properties
- is faithful
- is a reflector
- is a coreflector
- is representable
Deduced properties
- is a left adjoint
- is right-invertible
- is a right adjoint
- preserves terminal objects
- is continuous
- preserves initial objects
- is cofinitary
- is left exact
- preserves products
- is essentially surjective
- is cocontinuous
- preserves finite products
- preserves equalizers
- preserves monomorphisms
- is dominant
- is finitary
- preserves coproducts
- is right exact
- preserves binary products
- is exact
- preserves coreflexive equalizers
- preserves regular monomorphisms
- preserves finite coproducts
- preserves coequalizers
- preserves epimorphisms
- preserves binary coproducts
- preserves reflexive coequalizers
- preserves regular epimorphisms
- is coregular
- is regular
Unsatisfied Properties
Assigned properties
- is not essentially injective
- is not conservative
Deduced properties*
- is not fully faithful
- is not left-invertible
- is not full on isomorphisms
- is not pseudomonic
- is not monadic
- is not comonadic
- is not an equivalence
- is not full
- is not an isomorphism
*This also uses the deduced satisfied properties.
Unknown properties
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Comments
- This functor has exactly two right inverses (up to isomorphism), see MSE/4368730.