Derived Functors

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Related lectures (32)

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Functor Categories Composition and Induced Functors

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

Derived functors: Two technical lemmas

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

Derived Functor Approach

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

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

Quillen pairs and Quillen equivalences: Derived functors

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

Divisibility and Torsion

Explores divisibility and torsion in group theory, focusing on defining a functor that preserves divisibility.

Derived Functors in Homotopical Algebra

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

Existence of Left Derived Functors

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

Injective Modules: Ox-Modules and Injectives

Covers injective modules, Ox-modules, and their relevance in algebraic structures, emphasizing their importance in resolving acyclic resolutions and computing cohomology.

Adjunctions and Functor Categories: Exploring Connections

Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.