4
votes
In a monoidal category with duals is the coevaluation map determined by the evaluation?
If $(e,c)$ and $(e,c')$ both satisfy the snake equations, then $c=c'$:
However, for an arbitrary morphism $E:V^*\otimes V\to 1$ there is no reason to expect that there should exist a $C:1\to V\otimes ...
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