Quotient Spaces: Three Ways

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Related lectures (31)

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Serre model structure on Top

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

Unifying left and right homotopy: The homotopy relation

Explores the equivalence of left and right homotopy for morphisms between bifibrant objects.

Universal Covering Construction

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

Quasi-Categories: Active Learning Session

Covers fibrant objects, lift of horns, and the adjunction between quasi-categories and Kan complexes, as well as the generalization of categories and Kan complexes.

Quasicategories and Homotopy Categories

Covers the construction of homotopy categories from quasicategories, including definitions, compositions, and homotopy relations.

Homotopy Category of a Model Category

Introduces the homotopy category of a model category with inverted weak equivalences and unique homotopy equivalences.

Elementary Properties of Model Categories

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

Sets of Left Homotopy Classes: The Homotopy Relation in a Model Category

Explores sets of left homotopy equivalence classes of morphisms in model categories.

Homotopy Classes and Group Structures

Explores wedges in pointed spaces, group structures, and the Echman-Hilton argument.

Base B for the covering

Explores constructing a base B for a topology using homotopy classes and paths.