Covers of Acts Over Monoids and Pure Epimorphisms

In 2001, Enochs's celebrated flat cover conjecture was finally proven, and the proofs (two different proofs were presented in the same paper) have since generated a great deal of interest among researchers. The results have been recast in a number of other categories and, in particular, for add...

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Bibliographic Details
Published in:Proceedings of the Edinburgh Mathematical Society 2014-10, Vol.57 (3), p.589-617
Main Authors: Bailey, Alex, Renshaw, James H.
Format: Article
Language:English
Subjects:
Additives
Algebra
Categories
Equivalence
Flats
Mathematical analysis
Monoids
Proving
Theorems
Torsion
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Summary:In 2001, Enochs's celebrated flat cover conjecture was finally proven, and the proofs (two different proofs were presented in the same paper) have since generated a great deal of interest among researchers. The results have been recast in a number of other categories and, in particular, for additive categories. In 2008, Mahmoudi and Renshaw considered a similar problem for acts over monoids but used a slightly different definition of cover. They proved that, in general, their definition was not equivalent to that of Enochs, except in the projective case, and left open a number of questions regarding the ‘other’ definition. This ‘other’ definition is the subject of the present paper and we attempt to emulate some of Enochs's work for the category of acts over monoids, and concentrate, in the main, on strongly flat acts. We hope to extend this work to other classes of acts, such as injective, torsion free, divisible and free, in a future report.
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091513000618