forgetful functor for topological spaces
- notation: : →
- Source: category of topological spaces
- Target: category of sets
- Left adjoint:
- nLab Link
This functor maps a topological space to its underlying set .
Satisfied Properties
Assigned properties
- is faithful
- is representable
- is essentially surjective
- is a left adjoint
Deduced properties
- is continuous
- is cocontinuous
- is a right adjoint
- is cofinitary
- is left exact
- preserves products
- is finitary
- preserves coproducts
- is right exact
- preserves finite products
- is exact
- preserves equalizers
- preserves monomorphisms
- preserves finite coproducts
- preserves coequalizers
- preserves epimorphisms
- preserves terminal objects
- preserves coreflexive equalizers
- preserves initial objects
- preserves reflexive coequalizers
Unsatisfied Properties
Assigned properties
- is not essentially injective
- is not conservative
Deduced properties*
- is not full
- is not left-invertible
- is not monadic
- is not comonadic
- is not an equivalence
*This also uses the deduced satisfied properties.
Unknown properties
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