I think about the identities in monoidal categories $C$ (triangle and pentagon) the following way: Let $\Sigma=(\otimes,1)$ denote the monoid signature, $T(\Sigma,C_0)$ the set of terms over $\Sigma$ with objects from $C$ as variables and $\epsilon$ the evaluation map from terms to objects. Then, to any equivalent terms $s\sim t$ in $T(\Sigma,C_0)$ we can assign an isomorphism $f_{s,t}:\epsilon(s)\rightarrow\epsilon(t)$ such that for $s\sim t\sim u$ we have $f_{t,u}\circ f_{s,t}=f_{s,u}$. The triangle and pentagon identities form a kind of locally finite generator set for these isomorphism.
The definition of units and counits looks similar at first glance to the the definition of associators and unitors, however, our maps are not necessarily isomorphisms this time. So I wondered, does a similar finite generator set approach exist for the equations behind dual objects?