Mittag-Leffler modules and definable subcategories II
摘要
A countably generated module is Mittag-Leffler if and only if it is pure-projective, i.e., a direct summand of a direct sum of finitely presented modules. Trying to generalize this description to countably generated relative Mittag-Leffler modules, one runs into serious obstacles. The last theorem of Part I of the same title describes them as what was called uniform relative pure epimorphic images of a specific kind of ω-limits of finitely presented modules. A second part of this theorem attempted to make the ω-limits in question more concrete. In the formulation the application of those uniform pure epimorphisms was erroneously omitted. Correcting this led to a better result to be presented here. It states that under a mild assumption on the context, every countably generated relative Mittag-Leffler module ‘in the context’ is a direct summand of a certain preenvelope of a union of a relatively pure ω-chain of finitely presented modules. In conclusion a number of examples are presented that start with and grew out of the study of