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Related lectures (32)
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Cylinder Construction on Chain Complex
Explores the cylinder construction on a chain complex and its equivalence to chain homotopy.
Model Categories: Properties and Structures
Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.
Chain Homotopy and Projective Complexes
Explores chain homotopy, projective complexes, and homotopy equivalences in chain complexes.
Homotopy theory of chain complexes
Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.
Homotopy Category and Derived Functors
Explores the homotopy category of chain complexes and the relation between quasi-isomorphisms and chain homotopy equivalences.
Homotopy Equivalence in Chain Complexes
Explores homotopy equivalence in chain complexes, emphasizing path object construction and left/right homotopy characterization.
Elementary Properties of Model Categories
Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.
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.
The Whitehead Lemma: Homotopy Equivalence in Model Categories
Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.
Induced Homomorphisms on Relative Homology Groups
Covers induced homomorphisms on relative homology groups and their properties.
