Derived and triangulated categories (B. Keller)
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Lecture 1:
Additive categories, representable functors, abelian categories,
characterization of module categories, the full embedding theorem.

Lecture 2: 
Categories of complexes, derived categories, examples from
representation theory: derived categories of Dynkin quivers,
of the Kronecker quiver.

Lecture 3:
Derived functors, examples, triangulated categories, examples
(stable categories, derived categories), Morita theory for derived 
categories, subordinate invariants,

Lecture 4: 
t-structures, link with tilting theory, comparison of abelian 
categories with equivalent derived categories, piecewise
hereditary algebras.