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Related lectures (32)

Page 3 of 4

Introduction to Left Homotopy: The Homotopy Relation in a Model Category

Introduces left homotopy between morphisms and its preservation under postcomposition in a model category.

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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.

Homotopy Category and Derived Functors

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

Excision Theory: Sketch of Proof

Outlines the proof of the excision theory using the barycentric subdivision.

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

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

Homotopies & Equivalence Relations

Covers homotopies, fundamental group, and equivalence relations in applications.

Homotopy Classes and Group Structures

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

Homotopy: Degree

Covers the concept of degree in homotopy theory and the structure of complexes with two simplices.

Base B for the covering

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