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category-theory-presentation/categories/30_How/200_Monads/090_Necessary_laws.md
Yann Esposito (Yogsototh) 60135c8697 initial commit see my ykeynote repo for history
2013-02-28 16:49:12 +01:00

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Necessary laws

For ◎ to work like composition, we need join to hold the following properties:

  • join (join (F (F (F a))))=join (F (join (F (F a))))
  • abusing notations denoting join by ⊙; this is equivalent to
    (F ⊙ F) ⊙ F = F ⊙ (F ⊙ F)
  • There exists η :: a -> F a s.t.
    η⊙F=F=F⊙η