Lifting Properties in Model Categories: An Overview

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Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

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

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

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.

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

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

Covers limits and colimits, focusing on equalizers and coequalizers in category theory.

Covers morphisms with lifting properties, pushouts, pullbacks, and the uniqueness in the universal property of pushouts.

Explores lifting properties and model categories in topological spaces.

Focuses on lifting properties in homotopy theory of chain complexes.