rational product functor
This functor maps a topological space to the topological space , where carries the usual topology. It is a typical example of a functor that preserves epimorphisms but not regular epimorphisms.
Satisfied properties
Assigned properties
- is cofinitary
- preserves equalizers
- preserves monomorphisms
- preserves coproducts
- is dominant
- preserves epimorphisms
- is conservative
Deduced properties
- preserves coreflexive equalizers
- preserves regular monomorphisms
- is faithful
- preserves finite coproducts
- preserves binary coproducts
- preserves initial objects
Unsatisfied properties
Assigned properties
- does not preserve terminal objects
- does not preserve binary products
- is not essentially surjective
- is not finitary
- does not preserve regular epimorphisms
- is not essentially injective
Deduced properties*
- is not a reflector
- is not an equivalence
- does not preserve finite products
- is not regular
- is not left-invertible
- is not right-invertible
- is not full on isomorphisms
- is not cocontinuous
- does not preserve coequalizers
- does not preserve reflexive coequalizers
- is not an isomorphism
- does not preserve products
- is not left exact
- is not full
- is not pseudomonic
- is not a left adjoint
- is not a coreflector
- is not right exact
- is not continuous
- is not exact
- is not fully faithful
- is not coregular
- is not comonadic
- is not a right adjoint
- is not representable
- is not monadic
*This also uses the deduced satisfied properties.
Unknown properties
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