Brian Beckman: Don’t Fear the Monad

  • A monoid is: ({stuff}, operations)  where the operations are associative and have a unit.
    http://25.media.tumblr.com/8796d491890057c0ab488ccf4589fc34/tumblr_mpck6hmZC11qc38e9o1_1280.jpg
  • So a monoid is a semigroup with unit. (a +0 or a ×1 or a 1_C ⟳)
  • Brian Beckman in this video expresses a monoid with two functions f:a->a and g:a->a. (same type or domain)
    image
    b∘a∘b∘a∘b∘a∘b∘a∘b∘a[⬟]
    image

    successor function and square function

    image

  • His example is addition mod 12 (integral hours on a clock).

    imageimage
  • Then the monoidal category happens when you allow f:a->b and g:b->c. (linking together different types or domains)
    image

(por jasonofthel33t)

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