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Lecture
Quillen Equivalences
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Homotopy Categories: Model Structures
Explores homotopy categories in model structures, emphasizing weak equivalences and the Whitehead Lemma.
Elementary Properties of Model Categories
Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.
Homotopy Coherent Groups and Quasi-Categories
Covers the characterization of trivial Kan fibrations and the importance of homotopy coherent groups.
Why Quasicategories?
Discusses the benefits of quasi-category theory and model structures.
Homotopy Category of a Model Category
Introduces the homotopy category of a model category with inverted weak equivalences and unique homotopy equivalences.
Model Categories and Homotopy Theory: Functorial Connections
Covers the relationship between model categories and homotopy categories through functors preserving structural properties.
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.
Model Category: Definition and Elementary Properties
Covers the definition and properties of a model category, including fibrations, cofibrations, weak equivalences, and more.
Derived functors: Two technical lemmas
Covers two technical lemmas essential for the Fundamental Theorem in homotopical algebra.
