The concept of elementary epimorphism is introduced. Inverse systems of such maps are considered, and a dual of the elementary chain lemma is found (Cor. 4.2). The same is done for pure epimorphisms (Cor. 4.3 and 4.4). Finally, this is applied to certain inverse limits of flat modules (Thm. 6.4) and certain inverse limits of absolutely pure modules (Cor. 6.3).
"Elementary epimorphisms." J. Symbolic Logic 70 (2) 473 - 487, June 2005. https://doi.org/10.2178/jsl/1120224724