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Apr 2 at 13:11 comment added Yilmaz Caddesi However for vector spaces and projective modules it seems to work . . . so I guess it works in general for reasons that I cannot see . . .
Apr 2 at 10:55 comment added Yilmaz Caddesi If I write $e_{\sigma} := e \circ (id \otimes \sigma^{-1})$ and $c_{\sigma} := (\sigma \otimes \mathrm{id}) \circ c$, then the relation $(id \otimes e_{\sigma}) \circ (c_{\sigma} \otimes id) = id$ does not seem to be satisfied, since the $\sigma$ and $\sigma^{-1}$ are in the wrong place for cancellation. Hence $e_{\sigma}$ and $c_{\sigma}$ do not satisfy the axioms of dual object.
Apr 2 at 1:05 history answered S. Carnahan CC BY-SA 4.0