Hopf joke? (HW from class on April 5)

What did 0 say to 8?

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7 comments

  1. (Here’s my wild stab at it.)

    Nice coproduct!

    (Refer to page 9 of the lecture notes on the incidence coalgebra.)

  2. Playing off the “nice belt” comment from yesterday’s class: “You’re no poset!”

    (Violation of the antisymmetry criteria.)

  3. “You ought to get blown up.”

    Oh wait, it’s not supposed to be an algebraic geometry joke.

    Julia: how are you checking the antisymmetry of the set 8? 😮

    • I didn’t see this comment until much later, but I was imagining 8 to be a poset-looking-thing with a top element and a bottom element and two elements on the same level in the middle, both connected to one another, and antisymmetry specifically prohibits horizontal connections.

      • @Julia: ah! When I think of an 8, it usually has just one point in the middle. That would be a poset, even a ranked one.

      • Most definitely. It depends on how you draw it – like a sideways infinity or like a theta. (and we never see them drawn as thetas unless they’re on a numeric LED)

        The context for this is when Federico told his Hopf joke in class, it implied that an 8 was a 0 with a belt. That’s where I got the visual from.

  4. Here’s an unrelated Hopf joke:

    What did Santa Claus say to the bialgebra \mathbb{K} G, where G = 2^S for some finite set S, on Christmas day? “Hopf, Hopf, Hopf! You’ve been a bad bialgebra, so there’s no antipode for you!”

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