The integers have TWO KINDS of multiplications (OR MORE??)

Comments · 487

• NO

  @NoLongerBreathedIn · 1 year ago (edited) · pinned

  <a href="https://www.youtube.com/watch?v=2lK2X_f2BhA&amp;t=889">14:49</a> it doesn&apos;t - consider the case when all three vector spaces are ℂ^0|1 (the odd complex line). Then braiding V over U×W braids fermion over boson, so the multiplier is 1, but braiding it over U and W separately gives multipliers of e^i for each. So the hexagonators don&apos;t close up.<br><br>To fix this, give the vector spaces ℤ gradings instead, and say that β(v×w) = e^(i*gr(v)*gr(w)) w×v. This works fine.<br><br>If you want to only have a finite amount of grades, use GF(3) and do things in the obvious way (see under ℤ gradings); just make sure that the phase-shifts are by ⅓ rotations.

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• NA

  @Nameless.Individual · 1 year ago

  Came to enjoy a mathematician struggle with C/C++, stayed for the insane ramblings of a category theorist.

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• MA

  @maxdiabolo · 1 year ago

  But G, this video is completely comprehensible. My crippeling desire to be dumbfounded by abstract nonsense is not impressed by your puny &apos;uhh actually some compositions are not commutative&apos; and &apos;ahh coffee mugs are topologicaly equivalent to a...&apos; wait... <a href="https://www.youtube.com/watch?v=2lK2X_f2BhA&amp;t=528">8:48</a> Monoid mentioned. Is that an arrow. Oh no.

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• CY

  @CyborusYT · 1 year ago

  I feel like an ant that&apos;s having taxes explained to it

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• EA

  @EastBurningRed · 1 year ago

  when people say “you should ask questions if you don’t understand something”, but I don’t even know what to ask

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• MA

  @mattcroft · 1 year ago

  This video exists in a very frustrating liminal space where I understand enough to sort of get the gist of where we are but not enough to have any idea of where we&apos;re going

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• TO

  @tomholroyd7519 · 1 year ago (edited)

  Two Multiplications walk into a bar. One is Cartesian, the other is Monoidal. Their e&apos;s meet, and they both Order the Residuated Lettuce

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• DE

  @Devotee_of_void · 1 year ago

  &quot;Bosonic&quot; and &quot;fermionic&quot; tell me much more then 90% of words in this video

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• BL

  @blandconstant5548 · 1 year ago

  higher category theory has to cause some sort of health problems im convinced

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• MA

  @maxmustermann5590 · 1 year ago

  <a href="https://www.youtube.com/watch?v=2lK2X_f2BhA&amp;t=275">4:35</a> after conditioning me to expect a deep question after the &apos;but geee&apos;, this hit hard lmao

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• DA

  @danielmurawski5926 · 1 year ago

  I&apos;m doing PhD in probability and this video is a strong argument for my hypothesis that all algebraists and topologists are high when they&apos;re doing their stuff. This has strong mad wizard in his wizard tower energy. Cheers

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• FO

  @ForsakenDAemon · 1 year ago

  “But algebras are sometimes free” is the kind of joke that I aspire to. Made me snort my coffee as I drank it from my doughnut.

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