Derived functors: Two technical lemmas

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

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

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

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

Introduces left and right derived functors in homotopical algebra, emphasizing their uniqueness and providing an illustrative example.

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

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

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

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

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