Category of p-Complete Abelian Groups
Fix a prime p. Denote the full subcategory of abelian groups whose objects are p-complete as Ab((p) over cap). It is well known that Ab((p) over cap) does not form an abelian subcategory of the category of abelian groups. This work does not treat Ab((p) over cap) as a subcategory, but as a category in its own right and asks how close Ab((p) over cap) is to an abelian category. We show Ab((p) over cap) 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.
Communications In Algebra
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Vanderpool, Ruth, "Category of p-Complete Abelian Groups" (2012). SIAS Faculty Publications. 231.