Cool, I suppose that it makes good enough sense to interpret *tonk* through the lens of an Abelian category. It is where my intuition goes as well, Gentzen gives the introduction rules as the unit to some adjunction and the elimination rules as the counit to some adjunction. Tonk-like connectives are exactly zero objects in that we get universal arrows to and from them, like zeros in homology. I will have to read further to see what the parallels are to the more traditional Abelian categories like homological algebra. Do we learn something by studying short exact sequences of deductions, beginning and ending with *tonk*?
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