scratch

§ Never Forget Monic Again

created 2021-08-19
  • Remember monic ~ injective.
  • Remember that injective is f(x)=f(y)  ⟹  x=yf(x) = f(y) \implies x = yf(x)=f(y)⟹x=y.
  • Since we're doing category theory, replace xxx and yyy by functions h(p)h(p)h(p) and k(p)k(p)k(p).
  • This means that the rule of monic is ∀p,f(h(p))=f(k(p))  ⟹  h=k\forall p, f(h(p)) = f(k(p)) \implies h = k∀p,f(h(p))=f(k(p))⟹h=k.
  • Thus, monic is left cancellative!
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