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Related lectures (32)

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Homotopy Theory of Chain Complexes

Explores the model structure on chain complexes over a field.

Cofibrations: Extension Property and Recognition Principle

Explores the extension property of spaces and the recognition principle for cofibrations.

Topology Seminar: Tower Sequences and Homomorphisms

Explores tower sequences, homomorphisms, and their applications in topology, including the computation of homology and the construction of telescopes.

Quillen pairs and Quillen equivalences: Derived functors

Explores Quillen pairs, equivalences, and derived functors in homotopical algebra.

Homotopy Category and Derived Functors

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

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes over a field, focusing on closure properties and decomposition.

Model Category: Definition and Elementary Properties

Covers the definition and properties of a model category, including fibrations, cofibrations, weak equivalences, and more.

Homotopy Extension Property

Demonstrates how to obtain homotopy equivalences between different spaces using the homotopy extension property.

Homotopic Extension Problem

Explores solving the homotopic extension problem, constructing relative CW complexes, and ensuring uniqueness in CW approximations.

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.