Convention 11.1.3. Let \(X\) be a dualizable object of \(C\). By condition (2) of Proposition 11.1.2, its dual represents the functor \(\Hom _C(-\otimes X,\unit )\colon C\catop \to \An \). In particular, the dual is unique, and we denote it by \(X^{\vee }\). An object representing this functor need not be a dual when \(X\) is not known to be dualizable; see the discussion of weak duals in Subsection 11.1.1.
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