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Lecture
Homotopy theory of chain complexes
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Related lectures (32)
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Quillen Equivalences
Explores Quillen equivalences, emphasizing the preservation of cofibrations and acyclic cofibrations.
Derived functors: Identity and Homotopy Categories
Explores derived functors in model categories, focusing on identity and homotopy categories.
Homotopy Theory of Chain Complexes
Explores the model structure on chain complexes over a field.
Elementary Properties of Model Categories
Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.
Simplicial and Cosimplicial Objects: Examples and Applications
Covers simplicial and cosimplicial objects in category theory with practical examples.
Limits and Colimits in Functor Categories
Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.
Algebraic Kunneth Theorem
Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.
Construction of the homotopy category
Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.
Quillen pairs and Quillen equivalences: Derived functors
Explores Quillen pairs, equivalences, and derived functors in homotopical algebra.
Quasi-Categories: Active Learning Session
Covers fibrant objects, lift of horns, and the adjunction between quasi-categories and Kan complexes, as well as the generalization of categories and Kan complexes.
