Categories of Modules and Homological Algebra 2026/27

Categories of Modules and Homological Algebra

Lectures:

(30.9.) 1. Exactnes. Preaditive categories and additive functors. Basic examples. Exact sequences of modules and short exact sequence. Hom functors are additive and left exact. [LS, 1.2.1-4, 2.1.1] 2. Projectivity and injectivity. Description of projectivity and injectivity by exactness.

(7.10.) Free modules are projective, splitting exact sequenses, charcterization of prejectivity by spliting property and free modules [LS, 1.3.1-6]. Baer's criterion of injectivity, divisbility, construction of injective modules via divisible abelian groups and Hom(R,-) Category of modules has enough injetives [LS, sections 2.2 and 2.3].

[LS] - Lecture notes of Liran Shaul