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Lecture
Cofibrations: Extension Property and Recognition Principle
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Elementary Properties of Model Categories
Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.
Derived functors: Identity and Homotopy Categories
Explores derived functors in model categories, focusing on identity and homotopy categories.
Homotopy Theory: Cylinders and Path Objects
Covers cylinders, path objects, and homotopy in model categories.
Model Categories: Properties and Structures
Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.
Homotopy Category of a Model Category
Introduces the homotopy category of a model category with inverted weak equivalences and unique homotopy equivalences.
Homotopy Theory of Chain Complexes
Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.
Group Actions: Quotients and Homomorphisms
Discusses group actions, quotients, and homomorphisms, emphasizing practical implications for various groups and the construction of complex projective spaces.
Model Category: Definition and Elementary Properties
Covers the definition and properties of a model category, including fibrations, cofibrations, weak equivalences, and more.
Homotopy Theory in Care Complexes
Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.
The Whitehead Lemma: Homotopy Equivalence in Model Categories
Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.
