A piece of improvisation on a handful of conversations about contravariant classes. A concise way of stating where the main argument leads to is: Divisible looks a lot like Alternative because both have a product on the argument side and a coproduct on the result side, with Divisible's coproduct being on Haskop; also, Decidable looks a lot like Applicative for analogous reasons. (I didn’t put it like that in the post because it was long enough already without an extra excursion through monoidal functor theory.)
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