indiscrete topology functor
This functor maps a set to the indiscrete topological space in which only the empty set and are open.
Satisfied Properties
Assigned properties
- is fully faithful
- preserves initial objects
- is a right adjoint
- preserves coequalizers
- is finitary
Deduced properties
- is continuous
- is faithful
- is full
- is conservative
- is left-invertible
- is monadic
- preserves reflexive coequalizers
- preserves regular epimorphisms
- is cofinitary
- is left exact
- preserves products
- is essentially injective
- is full on isomorphisms
- preserves epimorphisms
- 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 finite coproducts
- is not dominant
Deduced properties*
- is not essentially surjective
- does not preserve coproducts
- does not preserve binary coproducts
- is not right exact
- is not an equivalence
- is not exact
- is not right-invertible
- is not cocontinuous
- is not coregular
- is not a reflector
- is not an isomorphism
- is not a left adjoint
- is not a coreflector
- is not comonadic
- is not representable
*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 indiscrete topology functor. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.