In 1961, Jan-Erik Roos published a "theorem", which says that in an [AB4*] abelian category, lim1 vanishes on Mittag-Leffler sequences. See Propositions 1 and 5 in . This is a "theorem" that many people since have known and used. In this article, we outline a counterexample. We construct some strange abelian categories, which are perhaps of some independent interest. These abelian categories come up naturally in the study of triangulated categories. A much fuller discussion may be found in...[Show more]
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