Homotopy theory

Related lectures (32)

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Explores homotopy equivalence in chain complexes, emphasizing path object construction and left/right homotopy characterization.

Explores the model structure on chain complexes over a field.

Introduces the concept of a universal covering construction with examples like Hawaiian rings.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores the cylinder construction on a chain complex and its equivalence to chain homotopy.

Explores the cellular approximation theorem for CW complexes and its implications on homotopy groups.

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.

Covers homotopy type theory, including equivalences, contractible spaces, pushouts, and applications.