Corollary 23.3.3. A morphism of animae \(p\colon X \to Y\) is an equivalence if and only if all its fibers are contractible.
Proof. Since \(X\) is an anima, every morphism in \(X\) is an isomorphism, and in particular \(p\)-cocartesian. It follows that \(p\) is a left fibration, and thus the claim holds by the previous corollary. □
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