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Arguments working entirely at a high level of abstraction, particularly category-theoretic arguments.

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Ref request: making a homotopy equivalence fibrewise, in an abstract setting (eg fibration c...

The following useful lemma holds in a variety of settings: Lemma. Let $p : Y_1 \to X$, $p_2 : Y_2 \to X$ be fibrations over a common base, and $f : Y_1 \to Y_2$ a map over $X$ that is a homotopy equ …