ring idempotents functor
This functor sends a ring to its set of idempotent elements. A ring homomorphism restricts to a map . Among other things, it provides an example of a representable functor that does not preserve regular epimorphisms.
Satisfied properties
Assigned properties
- is representable
- is finitary
Deduced properties
- is a right adjoint
- is continuous
- is cofinitary
- is left exact
- preserves products
- preserves finite products
- preserves equalizers
- preserves monomorphisms
- preserves binary products
- preserves terminal objects
- preserves coreflexive equalizers
- preserves regular monomorphisms
Unsatisfied properties
Assigned properties
- is not faithful
- is not full
- is not essentially injective
- is not dominant
- does not preserve initial objects
- does not preserve binary coproducts
- does not preserve regular epimorphisms
Deduced properties*
- is not regular
- is not fully faithful
- is not conservative
- is not left-invertible
- is not full on isomorphisms
- is not pseudomonic
- is not essentially surjective
- is not monadic
- is not a coreflector
- does not preserve finite coproducts
- does not preserve coequalizers
- does not preserve epimorphisms
- does not preserve reflexive coequalizers
- is not comonadic
- is not an equivalence
- is not right-invertible
- does not preserve coproducts
- is not right exact
- is not a reflector
- is not an isomorphism
- is not exact
- is not cocontinuous
- is not coregular
- is not a left adjoint
*This also uses the deduced satisfied properties.
Unknown properties
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