Algebraic topology

Related lectures (32)

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Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.

Explores the model structure on chain complexes over a field.

Explores derived functors in model categories, focusing on identity and homotopy categories.

Covers homology with coefficients, introducing the concept of defining homology groups with respect to arbitrary abelian groups.

Covers cylinders, path objects, and homotopy in model categories.

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

Explores the homotopy category of chain complexes and the relation between quasi-isomorphisms and chain homotopy equivalences.

Covers the first properties of singular homology and the preservation of decomposition and path-connected components in topological spaces.

Covers the relationship between model categories and homotopy categories through functors preserving structural properties.

Covers the Zig Zag Lemma and the long exact sequence of relative homology.