Cohomology: Recollection and Foliations

Related lectures (32)

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

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

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

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

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

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

Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.

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

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

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