Category of p-Complete Abelian Groups

Publication Date

2012

Document Type

Article

Abstract

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.

Publication Title

Communications In Algebra

Volume

40

Issue

8

First Page

2949

Last Page

2961

DOI

10.1080/00927872.2011.587856

Publisher Policy

pre-print & post-print with 12- to 18- month embargo

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