The Whitehead Lemma: Homotopy Equivalence in Model Categories

This lecture presents the Whitehead Lemma, a fundamental result in homotopy theory, which states that a morphism between bifibrant objects in a model category is a weak equivalence if and only if it is a homotopy equivalence. The instructor proves this lemma step by step, showing how the concept of homotopy equivalence generalizes in the context of model categories. Through a detailed analysis of the proof, the lecture highlights the importance of bifibrant objects and the homotopy relation in establishing weak equivalences. The presentation emphasizes the analogy with classical homotopy theory of spaces, providing a deep understanding of the Whitehead Lemma and its implications.