Flat relative Mittag-Leffler modules and approximations

Abstract

The classes ${\mathcal{D}}_{\mathcal{Q}}$ of flat relative Mittag-Leffler modules are sandwiched between the class $\mathcal{F}\mathcal{M}$ of all flat (absolute) Mittag-Leffler modules, and the class $\mathcal{F}$ of all flat modules. Building on the works of Angeleri H\" ugel, Herbera, and \v Saroch, we give a characterization of flat relative Mittag-Leffler modules in terms of their local structure, and show that Enochs' Conjecture holds for all the classes ${\mathcal{D}}_{\mathcal{Q}}$. In the final section, we apply these results to the particular setting of f-projective modules.

9 pages

References in corpus (1)

• Closure properties of $\underrightarrow{\lim }\mathcal{C}$

Cited by in corpus (3)

• Dualizations of approximations, ${\aleph }_1$-projectivity, and Vopěnka's Principles
• Flat Mittag-Leffler modules, and their relative and restricted versions
• Flat relative Mittag-Leffler modules and Zariski locality