Homological algebra 1981/82. For 4th year mathematics students. Official name: Algebra superiore.

MODULES OVER A COMMUTATIVE RING Motivations Modules over a ring Homomorphisms of modules Direct sums of modules Free modules CATEGORIES AND FUNCTORS Categories Functors Direct products and direct sums in categories Direct and inverse limits MULTILINEAR ALGEBRA Classical tensor calculus Tensor product of modules Comparison with the classical concept Tensor product of homomorphisms Tensor algebra Exterior algebra Determinants from exterior algebra PROJECTIVE AND INJECTIVE MODULES Exact sequences Two lemmas about free modules Projective modules Injective modules Exact functors, hom and tensor functors HOMOLOGY Complexes of modules An example from topology Homological border and the long exact sequence Homotopy of differential modules Projective and injective resolutions The idea of derived functor Theory of derived functors Final results on derived functors EXT AND TOR The two Exts coincide Some elementary properties of Ext Ext and projective and injective modules Extensions The two Tors coincide Some elementary properties of Tor Tor and projective modules SPECTRAL SEQUENCES Graded modules Differential homomorphisms Bigraded modules Exact couples and spectral sequences rEpq, rZpq, rBpq, Zpqi, Bpqi, Epqi (i = infinity) The exact couple associated to a filtered complex