Derived Functors in Homotopical Algebra

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

Explores the existence of left derived functors in homotopical algebra, focusing on isomorphism conditions and natural transformations.

Explores the left homotopy relation as an equivalence relation in model categories.

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

Focuses on proving the construction of the homotopy category and its properties, including preservation of composition and uniqueness of functors.

Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.

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

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

Covers the transfer of model structures through adjunctions in the context of model categories.

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