Weak equivalence (homotopy theory)

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Related lectures (32)

Explores the push out product concept and its application in vibrations, setting the stage for understanding homotopy invariants.

Universal Covering Construction

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

Base B for the covering

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

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.

Group Actions: Quotients and Homomorphisms

Discusses group actions, quotients, and homomorphisms, emphasizing practical implications for various groups and the construction of complex projective spaces.

Quillen pairs and Quillen equivalences: Derived functors

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

Lifting Properties in Model Categories: An Overview

Provides an overview of lifting properties in model categories, focusing on their definitions and implications for morphisms and commutative diagrams.

Homotopy Invariance

Explores homotopy invariance, emphasizing the preservation of properties under continuous functions and their relationship with topological spaces.

The Topological Künneth Theorem

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

CW Approximation Uniqueness

Explores the uniqueness of CW approximation and Whitehead's theorem through the construction of maps inducing isomorphisms on homotopic groups.

Homology Theorem

Covers the proof of Theorem A, discussing homology, quotients, and isomorphisms.

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