discrete topology functor
- Notation:
- Domain: category of sets
- Codomain: category of topological spaces
- Right adjoint functor:
- Related functors:
- nLab Link
This functor maps a set to the discrete topological space in which every subset is open. It is a typical example of a fully faithful functor that preserves finite but does not preserve infinite products.
Satisfied Properties
Assigned properties
- is fully faithful
- is a left adjoint
- preserves finite products
- preserves equalizers
Deduced properties
- preserves binary products
- preserves terminal objects
- is left exact
- preserves coreflexive equalizers
- preserves regular monomorphisms
- is faithful
- is full
- is conservative
- is cocontinuous
- is comonadic
- is left-invertible
- preserves monomorphisms
- is essentially injective
- is full on isomorphisms
- is finitary
- preserves coproducts
- is right exact
- is exact
- is pseudomonic
- preserves finite coproducts
- preserves coequalizers
- preserves epimorphisms
- is coregular
- preserves binary coproducts
- preserves initial objects
- preserves reflexive coequalizers
- preserves regular epimorphisms
- is regular
Unsatisfied Properties
Assigned properties
Deduced properties*
- is not continuous
- is not cofinitary
- is not essentially surjective
- is not a right adjoint
- is not an equivalence
- is not representable
- is not right-invertible
- is not a reflector
- is not an isomorphism
- is not monadic
- is not a coreflector
*This also uses the deduced satisfied properties.
Unknown properties
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Indistinguishable functors
These functors in the database currently have exactly the same properties as the discrete topology functor. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.