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Related lectures (32)
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Elementary Properties of Model Categories
Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.
Homotopy Theory of Chain Complexes
Explores the model structure on chain complexes over a field.
Derived functors: Identity and Homotopy Categories
Explores derived functors in model categories, focusing on identity and homotopy categories.
Homology with coefficients
Covers homology with coefficients, introducing the concept of defining homology groups with respect to arbitrary abelian groups.
Homotopy Theory: Cylinders and Path Objects
Covers cylinders, path objects, and homotopy in model categories.
Homology of Riemann Surfaces
Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.
Homotopy Category and Derived Functors
Explores the homotopy category of chain complexes and the relation between quasi-isomorphisms and chain homotopy equivalences.
Singular Homology: First Properties
Covers the first properties of singular homology and the preservation of decomposition and path-connected components in topological spaces.
Model Categories and Homotopy Theory: Functorial Connections
Covers the relationship between model categories and homotopy categories through functors preserving structural properties.
Zig Zag Lemma
Covers the Zig Zag Lemma and the long exact sequence of relative homology.