Abstract
Fix a prime p. Denote the full subcategory of abelian groups whose objects are p-complete as . It is well known that does not form an abelian subcategory of the category of abelian groups. This work does not treat as a subcategory, but as a category in its own right and asks how close is to an abelian category. We show satisfies all the axioms of an abelian category except the condition that all monics are kernels. We show the Five Lemma with epi arrows still holds whereas the Five Lemma with monic arrows does not.
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