Seminare on Cotorsion Theory

ZCC
July 20, 2025

Lectures

Lecture0. The preliminaries (basicc ring theories, complexes, etc.).

Lecture1. Orthogonality, cotorsion theory, complete cotorsion pairs. Ordinal and cardinals, small object, and Eklof-Trlifaj’s criterion.

Lecture2. Kaplansky class for reconstructing cogenerating sets, DG construction on cotorsion pairs, complete herediatary cotorsion paris and triples.

Lecture3. All cover/envelope theory studies projective covers. The defect of projective modules in covering theory. A criterion when (special) precover/preenvelope admits a (special) cover/envelope.

Lecture4. Definable subgroups, purity, and associated cotorsion theory.