Axiom J (Joyal). Let \(F,G\colon C \to D\) be two functors and let \(\alpha \colon F \Rightarrow G\) be a natural transformation. Then \(\alpha \) is a natural isomorphism if and only if for every object \(x\) of \(C\) the morphism \(\alpha (x)\colon F(x) \to G(x)\) is an isomorphism in \(D\).
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