Homotopy Theory: Cylinders and Path Objects

Related lectures (32)

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Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.

Explores the Serre model structure, focusing on left and right homotopy equivalences.

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.

Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.

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

Explores the homotopy theory of chain complexes, focusing on defining cylinder objects and left homotopy.

Explores homotopy categories in model structures, emphasizing weak equivalences and the Whitehead Lemma.

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

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.