Lectures related to Ext functor

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

Covers the basics of Homological algebra, focusing on Ext modules and their significance in modern mathematics.

Covers exact sequences in homological algebra and the properties of Hom functors.

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

Covers the construction of long exact sequences of Ext-modules and provides illustrative examples.

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

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

Explores the long exact sequence of Ext-modules and their computations in homological algebra.

Covers free resolution of modules and projective modules in module theory.

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

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.

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

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

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

Explores the joint equidistribution of CM points for cubic fields, emphasizing periodic orbits and quadratic algebraic forms.

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

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

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

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