Remark 11.1.14. The objects called dualizable here are called strongly dualizable in Lewis et al. (1986), Chapter III, Definition 1.1. That reference also gives the following useful criterion: if \(C\) is closed, then \(X\) is dualizable precisely when the morphism \(\unit \to \iHom (X,X)\) adjoint to \(\id _X\) factors through the natural map \(X\otimes D(X)\to \iHom (X,X)\).
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