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Lecture
Existence of Left Derived Functors
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Introduction to Derived Functors: Left and Right Derived Functors
Introduces left and right derived functors in homotopical algebra, emphasizing their uniqueness and providing an illustrative example.
Derived functors: Two technical lemmas
Covers two technical lemmas essential for the Fundamental Theorem in homotopical algebra.
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.
Derived functors: Identity and Homotopy Categories
Explores derived functors in model categories, focusing on identity and homotopy categories.
Existence of Left Derived Functors: Part 2
Concludes the proof of the existence of left derived functors and discusses total left and right derived functors.
Homotopical Algebra: Examples and Adjunctions
Explores homotopical algebra examples and adjunctions, focusing on left and right adjoints in group functors and coproducts.
Homotopical Algebra: (Co)Limits
Explores the concept of (co)limits in homotopical algebra, discussing functor relations, special cases, and the universal properties of colimits and limits.
Construction of the homotopy category
Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.
Group Cohomology
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
