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Related lectures (32)

Serre model structure: Left and right homotopy

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

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.

Topology: Homotopy and Projective Spaces

Discusses homotopy, projective spaces, and the universal property of quotient spaces in topology.

Model Categories and Homotopy Theory: Functorial Connections

Covers the relationship between model categories and homotopy categories through functors preserving structural properties.

Homotopy Theory: Cylinders and Path Objects

Covers cylinders, path objects, and homotopy in model categories.

Retracte: Fundamental Group and Cell Attachment

Covers the concept of a subspace being a retract of another space and fundamental groups, including examples like contracting the teeth of a necklace.

Homotopy theory of chain complexes

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

Contracting Subspaces

Explores the homotopy extension property for contractable subspaces and their quotient maps.

Homotopy Extension Property

Introduces the homotopy extension property, exploring conditions for extending continuous maps.

Pointed Mapping Spaces: Exponential Law and Adjunction

Explores pointed mapping spaces, the exponential law, adjunction properties, and homotopic classes.

Model Categories: Properties and Structures

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

Invariant Definitions

Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.

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