Introduction to homological algebra

MARIANO SUÁREZ-ALVAREZ

Curitiba

Congreso; Algebraic and Geometric Aspects of Representation Theory; 2013

CIMPA

This course aims at introducing the students to the basic notions of homological algebra, approached first from from an elementary viewpoint using derived functors and then using the notion of triangulated category and derived category. We start with a review of functors and categories including several examples and emphasizing the definitions of kernel and cokernel, product and coproduct, as well as the notions of right and left exact functors. Then we will talk about additive categories, the category of complexes of an additive category and the corresponding homotopy category. This will give rise to the notion of derived category.