p-torsion functor

notation: $T_p$ : $\Ab$ → $\Ab$
Source: category of abelian groups
Target: category of abelian groups
Left adjoint: $T^p$
Related functors: $T$

This functor maps an abelian group $A$ to its $p$ -torsion subgroup $T_p(A) \coloneqq \{a \in A : pa = 0\},$ where $p$ is a fixed prime number. This group can also be represented as $\HomInternal(\IZ/p,A)$ .

Satisfied Properties

Assigned properties

is a right adjoint
preserves coproducts
is finitary

Deduced properties

is continuous
preserves finite coproducts
is cofinitary
is left exact
preserves products
preserves initial objects
preserves finite products
preserves equalizers
preserves monomorphisms
preserves terminal objects
preserves coreflexive equalizers

Unsatisfied Properties

Assigned properties

is not essentially injective
is not essentially surjective
is not faithful
is not full
does not preserve epimorphisms
is not representable

Deduced properties*

is not an equivalence
is not conservative
is not left-invertible
is not monadic
is not right exact
does not preserve coequalizers
is not comonadic
is not exact
is not cocontinuous
does not preserve reflexive coequalizers
is not a left adjoint

*This also uses the deduced satisfied properties.

Unknown properties

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