Strict Mittag-Leffler modules and purely generated classes

TL;DR

This paper explores strict Mittag-Leffler modules relative to a class of modules, extending previous work on Mittag-Leffler modules and definable subcategories to include strict versions in this research series.

Contribution

It introduces and analyzes strict $ ext{Mittag-Leffler}$ modules relative to a class $ ext{K}$, providing new insights into their structure and properties compared to classical modules.

Findings

Development of the theory of strict $ ext{K}$-Mittag-Leffler modules

Extension of previous results on Mittag-Leffler modules and definable subcategories

New characterizations of strict Mittag-Leffler modules

Abstract

We study versions of strict Mittag-Leffler modules relativized to a class $\cK$ (of modules), that is, \emph{strict} versions (in the technical sense of Raynaud and Gruson) of $\cK$-Mittag-Leffler modules, as investigated in the preceding paper, {\em Mittag-Leffler modules and definable subcategories}, in this very series (as well as the arXiv).