Homotopy Lifting Property

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Related lectures (32)

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Cylinder Construction on Chain Complex

Explores the cylinder construction on a chain complex and its equivalence to chain homotopy.

CW Pairs: Homotopy Extension Property

Discusses how CW pairs satisfy the homotopy extension property through retractions and homotopy extension properties.

Homotopy theory of chain complexes

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

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.

Homotopic Extension Problem

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

Cohomology Representations: Lecture 14.1

Covers the concept of cohomology representations and the implications of reduced suspension operations on spaces.

Attachment of a 2-cell

Covers the attachment of a 2-cell to a space and explores the concept of the attachment application f.

Model Category: Definition and Elementary Properties

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

Topology: Lecture Notes 2021

Covers commutative diagrams, homotopy, and constructing topological spaces.

Homotopical Algebra: Introduction

Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.