Department Mathematik
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Inhaltsbereich
Homological Algebra I

Lecture 1 (part 1) (1,3 Gb, 41mn), Lecture 1 (part 2) (1,4 Gb, 43mn) :
Categories and functors.
Lecture 2 (part 1) (1,4 Gb, 45mn), Lecture 2 (part 2) (900 Mb, 30mn) :
Natural transformations, equivalences of categories, examples.
Lecture 3 (part 1) (1,1 Gb, 37mn), Lecture 3 (part 2) (1,2 Gb, 41mn) :
Adjoint functors, examples. Products.
Lecture 4 (part 1) (1,6 Gb, 53mn), Lecture 4 (part 2) (730 Mb, 25mn) :
Coproducts. Equalizers. Examples.
Lecture 5 (part 1) (1,2 Gb, 41mn), Lecture 5 (part 2) (1 Gb, 34mn) :
Coequalizers, (co-)limits. Examples.
Lecture 6 (part 1) (1,1 Gb, 36mn), Lecture 6 (part 2) (1,2 Gb, 39mn) :
(co-)limits; existence. Examples. Commutation of adjoint functors to (co-)limits.
Lecture 7 (part 1) (1,4 Gb, 48mn), Lecture 7 (part 2) (730 Mb, 25mn) :
(co-)limits of presheaves and sheaves. Pointed categories, categories where finite sums = finite products .
Lecture 8 (part 1) (1,3 Gb, 43mn), Lecture 8 (part 2) (1 Gb, 35mn) :
Pre-abelian categories, commutative monoids, "addition" of morphisms. Examples.
Lecture 9 (part 1) (1 Gb, 33mn), Lecture 9 (part 2) (1,3 Mb, 45mn) :
Abelian categories, Kern, Coker, factorisation. Abelian group structure on the monoid of morphisms. Examples.
Lecture 10 (part 1) (1,6 Gb, 54mn), Lecture 10 (part 2) (840 Mb, 28mn) :
Limits and colimits in abelian categories. Category of sheaves of abelian groups, of modules over a sheaf of commutative ring.
Lecture 11 (part 1) (1,3 Gb, 43mn), Lecture 11 (part 2) (1,3 Mb, 45mn) :
Projective and injective objects. Example. Projective and injective resolutions.(End of the lecture)