Ep 32: The proof of the Fundamental Theorem, Chapter 2(d): Derived functors, Quillen pairs, and Quillen equivalences

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To conclude this introduction to model categories, we prove the Fundamental Theorem of homotopical algebra, establishing that a Quillen pair induces an adjunction of the corresponding homotopy categories, while a Quillen equivalence induces an equivalence of the homotopy categories.