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  • fully dualizable

dualizable object of a category

For \((X, \otimes, \one)\) a Monoidal category, right duals: existence of two morphisms \begin{align*} {\varepsilon}: X {}^{ \vee }\otimes X &\to \one &&\text{evaluation} \\ \eta: \one &\to X\otimes X {}^{ \vee }&&\text{coevaluation} ,\end{align*} along with some diagram.

Objects admitting a left and right dual admit a trace