torsion functor
This functor maps an abelian group to its torsion subgroup
Satisfied properties
Assigned properties
- preserves finite products
- preserves equalizers
- is finitary
Deduced properties
- preserves binary products
- preserves terminal objects
- is left exact
- preserves coreflexive equalizers
- preserves regular monomorphisms
- preserves finite coproducts
- preserves monomorphisms
- preserves initial objects
- preserves binary coproducts
- preserves coproducts
Unsatisfied properties
Assigned properties
- is not essentially injective
- is not dominant
- is not faithful
- is not full
- does not preserve epimorphisms
- does not preserve products
Deduced properties*
- is not continuous
- is not cofinitary
- 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 right exact
- does not preserve regular epimorphisms
- is not comonadic
- is not a right adjoint
- is not an equivalence
- is not exact
- is not representable
- is not regular
- is not right-invertible
- is not cocontinuous
- does not preserve coequalizers
- does not preserve reflexive coequalizers
- is not coregular
- is not a reflector
- is not an isomorphism
- is not a left adjoint
- is not a coreflector
*This also uses the deduced satisfied properties.
Unknown properties
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