so let e : x -> y be an epi between dualizable objects (or something...) in a symmetric monoidal finitely cocomplete k-linear category... ??...

??then consider... the mate of e... ??and the cokernel of that... and the mate of that... ??... and the cokernel of that... and the mate of that... ??? and whether that returns to the original?? or something?? ??is there a comparison map here to invert?? ??or something?? ...

??consider smfcc k-linear cat where all adjoints exist (or something...) and the loop always closes that way... ???...

??how well-defined is this loop-closure property, in general?? ... or something...