modulo p functor

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

This functor maps an abelian group $A$ to the quotient $T^p(A) \coloneqq A/pA$ , where $p$ is a fixed prime number. This group can also be represented as $A \otimes \IZ/p$ .

Satisfied Properties

Assigned properties

is a left adjoint
preserves products

Deduced properties

preserves finite products
is cocontinuous
preserves terminal objects
is finitary
preserves coproducts
is right exact
preserves finite coproducts
preserves coequalizers
preserves epimorphisms
preserves initial objects
preserves reflexive coequalizers

Unsatisfied Properties

Assigned properties

is not essentially surjective
is not essentially injective
is not faithful
is not full
does not preserve monomorphisms
is not cofinitary
is not representable

Deduced properties*

is not an equivalence
is not continuous
is not left exact
does not preserve equalizers
is not left-invertible
is not monadic
is not conservative
is not comonadic
is not a right adjoint
is not exact
does not preserve coreflexive equalizers

*This also uses the deduced satisfied properties.

Unknown properties

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