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Concept

Tor functor

Related lectures (20)

Concludes the proof of the existence of left derived functors and discusses total left and right derived functors.

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Covers the Fundamental Theorem of homotopical algebra, Quillen pairs, and derived functors.

Explores the existence of left derived functors in homotopical algebra, focusing on isomorphism conditions and natural transformations.

Covers two technical lemmas essential for the Fundamental Theorem in homotopical algebra.

Introduces left and right derived functors in homotopical algebra, emphasizing their uniqueness and providing an illustrative example.

Explores the homotopy category of chain complexes and the relation between quasi-isomorphisms and chain homotopy equivalences.

Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.

Explores the verification of the universal property of the product in GC and the existence of G-action functors.

Explores Quillen pairs, equivalences, and derived functors in homotopical algebra.

Explores composition of functors, induced functors, and preservation of commutative diagrams in category theory.

Explores torsion and divisibility in abelian groups, including p-divisible groups and their contrast with torsion elements.

Explores derived functors in model categories, focusing on identity and homotopy categories.

Covers homomorphisms, projective modules, and resolutions in chain complexes.

Explores derived functors, Ext-modules, Yoneda extensions, and derived categories in the context of extending modules.

Covers cohomology, injective resolutions, and acyclic objects in an abelian category.

Covers the derived functor approach to Čech cohomology, emphasizing the relationship between derived functors and sheaf theory.

Covers the relationship between model categories and homotopy categories through functors preserving structural properties.

Explores the verification of a Lie functor as a left adjoint, with natural transformations satisfying triangular identities and isomorphisms.

Covers simple modules, endomorphisms, and Schur's lemma in module theory.