modulo p functor
This functor maps an abelian group to the quotient , where is a fixed prime number. This group can also be represented as .
Satisfied Properties
Assigned properties
- is a left adjoint
- preserves products
Deduced properties
- preserves finite products
- is cocontinuous
- preserves binary products
- preserves terminal objects
- is finitary
- preserves coproducts
- is right exact
- preserves finite coproducts
- preserves initial objects
- preserves binary coproducts
- preserves coequalizers
- preserves epimorphisms
- preserves reflexive coequalizers
- preserves regular epimorphisms
Unsatisfied Properties
Assigned properties
- is not dominant
- is not essentially injective
- is not faithful
- is not full
- does not preserve monomorphisms
- is not cofinitary
Deduced properties*
- is not continuous
- is not left exact
- does not preserve regular monomorphisms
- is not fully faithful
- is not left-invertible
- is not full on isomorphisms
- is not pseudomonic
- is not essentially surjective
- is not monadic
- is not conservative
- is not comonadic
- is not a right adjoint
- is not an equivalence
- does not preserve equalizers
- is not exact
- is not representable
- does not preserve coreflexive equalizers
- is not regular
- is not right-invertible
- is not coregular
- is not a reflector
- is not an isomorphism
- is not a coreflector
*This also uses the deduced satisfied properties.
Unknown properties
—