discrete topology functor
- notation: : →
- Source: category of sets
- Target: category of topological spaces
- Right adjoint:
- nLab Link
This functor maps a set to the discrete topological space in which every subset is open.
Satisfied Properties
Assigned properties
Deduced properties
- preserves terminal objects
- is left exact
- preserves coreflexive equalizers
- preserves monomorphisms
- is conservative
- is essentially injective
- is faithful
- is cocontinuous
- is finitary
- preserves coproducts
- is right exact
- is comonadic
- is exact
- preserves finite coproducts
- preserves coequalizers
- preserves epimorphisms
- preserves initial objects
- preserves reflexive coequalizers
Unsatisfied Properties
Assigned properties
- does not preserve products
- is not representable
Deduced properties*
- is not continuous
- is not cofinitary
- is not a right adjoint
- is not monadic
- is not an equivalence
- is not essentially surjective
*This also uses the deduced satisfied properties.
Unknown properties
—