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To all the referees that keep saying "the paper does not contain many examples" and "it is unclear what the applications of [...] are": there is none. Zero. Ø. I will never focus on anything other than the inherent mathematical beauty of a monadic, self-referential question.
page 1 of the paper: "Transducers are classical computational devices that extend FSMs with the ability to produce output" page 10 of the paper: "...we have just proved that this boils down to a graded promonad, with the grading given by the monoidal category of states"
This might very well be the most exciting paper I've managed to write so far. Kudos to @iwilare who almost single-handedly pulled this bravura piece.
If you were alone in the woods, would you rather encounter a bear or a man? Plot twist: the bear is an applied category theorist
Inside you there are two wolves: one invents graph theory to solve the Konigsberg problem, the other informally moves terms around a series to solve the Basel problem. Inside you there are two wolves: both wolves are Leonhard Euler.
— The species must flow. He who controls the species controls the universe.
"Knowing that the Riemann-Hilbert correspondence is an equivalence of triangulated categories may feel empowering, but as a matter of technique, it is mere stardust compared with the power of being able to write in full the 2-dimensional universal property of a lax limit."
<<Just consult a score of recent textbooks; discard any that seem a little different from the rest; those that are alike except for variation in offences to the language in which they are written will give you what "tradition" is in its present phase.>> C. "Savage" Truesdell
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