Homotopy Categories: Model Structures

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Homotopy theory of chain complexes

Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

Derived functors: Identity and Homotopy Categories

Explores derived functors in model categories, focusing on identity and homotopy categories.

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 theory of chain complexes

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

Homotopy Theory: Cylinders and Path Objects

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

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.

Quillen Equivalences

Explores Quillen equivalences, emphasizing the preservation of cofibrations and acyclic cofibrations.

Model Categories: Properties and Structures

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

Lifting properties and model categories

Covers the study of lifting properties in categories, focusing on the left and right lifting properties.