Proposition 4.4.4. For a stable \(\infty \)-category \(C\), there exists a unique functor \[ \hom _C(-,-)\colon C\catop \times C \to \Sp \] that is exact in both variables and fits in a commutative triangle as follows:
Proof. Apply the previous proposition to the underlying prespectrum of \(X\). Since \(X\) is already a spectrum, spectrification fixes it. □
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