Syllabus
1. Category theory of modules: 1.1 Covariant and contravariant Hom functors, projective and injective modules, 1.2 Tensor product, flat modules, 1.3 Adjointness of Hom functors and tensor product, 1.4 Morita equivalence of rings and its characterization. 2.
Introduction to homological algebra: 2.1 Complexes, projective and injective resolutions, 2.2 Ext^n and Tor_n functors, 2.3 Long exact sequences for Ext and Tor, 2.4 Connections between Ext^1 and extensions of modules, 2.5 The homotopy category of complexes and derived categories, 2.6 Triangulated categories.
Annotation
Category theory of modules (covariant and contravariant Hom functors, projective and injective modules, tensor product, flat modules, adjointness of Hom functors and tensor product, Morita equivalence of rings and its characterization), introduction to homological algebra (complexes, projective and injective resolutions, Ext^n and
Tor_n functors, connections between Ext^1 and extensions of modules, derived and triangulated categories).