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Theofilos Tsantilas (Jul 21 2026 at 13:53):Hello everyone! I follow a lot of conversations on this topic and thought of starting my own for feedback. I am Theofilos Tsantilas (he/him) but you can call me teo/theo or whatever you find best. I am currently a PhD student in Athens, Greece.
Together with Vassilis Aravantinos-Sotiropoulos and my supervisor, @Christina Vasilakopoulou, we put our preprint On categories of monads and comonads in double categories on arxiv. There, we study under what assumptions could the categories of (co)monads in a double category have nice properties, resembling the ones (co)monoids over a monoidal category have, such as the existence of (co)free objects, (co)monadicity and local presentability.