p-torsion functor

 algebra
Notation Tp:Ab→AbT_p: \Ab \to \Ab Domain category of abelian groupsCodomain category of abelian groupsLeft adjoint modulo p functor Related TT

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

Satisfied Properties

Assigned properties

Deduced properties

Unsatisfied Properties

Assigned properties

Deduced properties*

*This also uses the deduced satisfied properties.

Unknown properties

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